Biography
Professor Andrea Mondino teaches first year Analysis Tutorials at St Hilda's College.
He has experience of teaching at every level from bachelor, master, to graduate level classes across Analysis and Geometry.
Professor Andrea Mondino works at the interface between Analysis and Geometry. More precisely he studies problems arising from (differential and metric) geometry by using analytic techniques such as optimal transport, functional analysis, partial differential equations, calculus of variations, gradient flows, nonlinear analysis, geometric measure theory. Although the emphasis of his work is primarily theoretical, the topics and the techniques have profound links with applications to natural sciences (mainly physics and biology) and economics.
PUBLICATIONS
1. A. Mondino, Some results about the existence of critical points for the Willmore functional, Math.Zeit., Vol. 266, Num. 3, (2010), pp. 583-622
2. A. Mondino, The conformal Willmore Functional: a perturbative approach, Journal of Geometric Analysis, Vol. 23, (2013), no. 2, pp. 764-811.
3. A. Mondino, The Willmore and other Lp curvature functionals in Riemannian manifolds, Ph. D. Thesis (2011), SISSA digital library.
4. N. Gigli, A. Mondino, A PDE approach to non linear potential theory, Journal de Mathematiques Pures et Appliquees, Vol. 100, (2013), no. 4, pp. 505-534.
5. A. Mondino, Existence of Integral m-Varifolds minimizing curvature integrals in Riemannian Man-ifolds, Calculus of Variations and Partial Differential Equations, Vol. 49, (2014), no. 1-2, pp. 431-470.
6. E. Kuwert, A. Mondino, J. Schygulla, Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds, Math. Annalen, Vol. 359, (2014), no. 1, pp. 379-425.
7. A. Mondino, T. Riviere, Immersed Spheres of Finite Total Curvature into Manifolds, Advances in Calculus of Variations, Vol. 7, (2014), no. 4, pp. 493-538.
8. A. Mondino, J. Schygulla, Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds, Annales de l'Institut Henri Poincare / Analyse non lineaire, Vol. 31, (2014), pp. 707-724.
9. A. Mondino, T. Riviere, Willmore Spheres in Compact Riemannian Manifolds, Advances in Mathematics, Vol. 232, (2013), no.1, pp. 608-676.
10. A. Carlotto, A. Mondino, Existence of generalized totally umbilic 2-spheres in perturbed 3-spheres, Int. Math. Res. Not., Vol. 2014, (2014), no. 21, pp. 6020-6052.
11. N. Garofalo, A. Mondino, Li-Yau and Harnack type inequalities in RCD(K,N) metric measure spaces , Nonlinear Analysis: Theory, Methods & Applications Vol. 95, (2014), pp. 721-734.
12. L. Keller, A. Mondino, T. Riviere, Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint, Arch. Rational Mech. Anal., Vol. 212, (2014), pp. 645-682.
13. A. Mondino, H. T. Nguyen, A Gap Theorem for Willmore Tori and an application to the Willmore Flow, Nonlinear Analysis: Theory, Methods & Applications, Vol. 102, (2014), pp. 220-225.
14. A. Mondino, A. Naber, Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds, Journal of European Math. Soc., Vol. 21, no. 6, (2019), pp. 1809-1854. DOI: 10.4171/JEMS/874.
15. P. Laurain, A. Mondino, Concentration of small Willmore spheres in Riemannian 3-manifolds, Analysis & PDE, Vol. 7, (2014), no. 8, pp. 1901-1921.
16. L. Ambrosio, N. Gigli, A. Mondino, T. Rajala, Riemannian Ricci curvature lower bounds in metric measure spaces with sigma-finite measure, Trans. Amer. Math. Soc. 367 (2015), no. 7, pp. 4661-4701.
17. N. Gigli, A. Mondino, T. Rajala, Euclidean spaces as weak tangents of infinitesimally Hilbertian metric spaces with Ricci curvature bounded below, Journal fur die Reine und Angew. Math. (Crelle's
journal), Vol. 705, (2015), pp. 233-244.
18. A. Mondino, A new notion of angle between three points in a metric space, Journal fur die Reine und Angew. Math. (Crelle's journal), Vol. 706, (2015), pp. 103-121.
19. N. Gigli, A. Mondino, G. Savare, Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows, Proc. London Math. Soc., Vol. 111, Num. 5, (2015), pp. 1071-1129.
20. A. Mondino, H. T. Nguyen, Global conformal invariants for submanifolds, Annales de l'Institut Fourier, Vol. 68 (2018), no. 6, pp. 2663-2695.
21. A. Mondino, S. Nardulli, Existence of Isoperimetric regions in non-compact Riemannian manifolds under Ricci curvature conditions, Communications in Analysis and Geometry, Vol. 24, (2016), no. 1, pp. 115-136.
22. A. Mondino, T. Riviere, A frame energy for immersed tori and applications to regular homotopy classes, Journal of Differential Geometry, Vol. 104, (2016), no.1, pp. 143-186.
23. L. Ambrosio, A. Mondino, G. Savare, On the Bakry- Emery condition, the gradient estimates and the Local-to-Global property of RCD(K,N) metric measure spaces, Journal of Geometric Analysis, Vol. 26, (2016), pp. 24-56.
24. A. Mondino, G. Wei, On the universal cover and the fundamental group of an RCD(K,N)-space, preprint arXiv:1605.02854, pp.1-26, (2016), to appear in Crelle, DOI: 10.1515/crelle-2016-0068
25. F. Cavalletti, A. Mondino, Measure rigidity of Ricci curvature lower bounds, Advances in Mathematics, Vol. 286, (2016), pp. 430-480.
26. L. Ambrosio, A. Mondino, Gaussian-type Isoperimetric Inequalities in RCD(K,\infty) probability spaces for positive K, Rend. Lincei Mat. Appl., Vol. 27, (2016), pp. 497-514
Special volume dedicated to the memory of E. De Giorgi.
27. N. Ikoma, A. Malchiodi, A. Mondino, Embedded area-constrained Willmore tori of small area in Riemannian 3-manifolds I: minimization, Proc. Lond. Math. Soc., Vol. 115, (2017), no. 3, pp. 502-544.
28. N. Ikoma, A. Malchiodi, A. Mondino, Embedded area-constrained Willmore tori of small area in Riemannian 3-manifolds II: Morse Theory, Amer. J. Math., Vol. 139, (2017), no. 5, pp. 1315-1378.
29. F. Cavalletti, A. Mondino, Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds, Inventiones Math., Vol. 208, (2017), no. 3, pp. 803-849.
30. F. Cavalletti, A. Mondino, Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds, Geometry & Topology, Vol. 21, (2017), no. 1, pp. 603-645.
31. A. Carlotto, A. Mondino, A non-existence result for minimal catenoids in asymptotically at spaces, Journal of London Math. Society, Vol. 95, (2017), no. 2, pp. 373-392.
32. F. Cavalletti, A. Mondino, Optimal maps in essentially non-branching spaces, Communications in Contemporary Math. Vol. 19, (2017), no. 6, 27 pp.
33. A. Mondino, E. Spadaro, On a isoperimetric-isodiametric inequality, Analysis and PDE, Vol. 10, (2017), no. 1, pp. 95-126.
34. L. Ambrosio, A. Mondino, G. Savare, Nonlinear diffusion equations and curvature conditions in metric measure spaces, preprint arXiv:1509.07273, pp. 1-115, (2015), to appear in Memoirs Amer. Math. Soc.
35. B. Han, A. Mondino, Angles between curves in metric measure spaces, Anal. Geom. Metr. Spaces, Vol. 5, (2017), pp. 47-68.
36. M. Kell, A. Mondino, On the volume measure of non-smooth spaces with Ricci curvature bounded below, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. 18, (2018), no. 2, 593-610.
37. C. Ketterer, A. Mondino, Sectional and intermediate Ricci curvature lower bounds via Optimal Transport, Advances in Math., Vol. 329, (2018), pp. 781-818.
38. F. Cavalletti, A. Mondino, Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds, International Mathematics Research Notices (IMRN), https://doi.org/10.1093/imrn/rny070. (2018), pp.1-30.
39. F. Cavalletti, F. Maggi, A. Mondino, Rigidity for critical points in the Levy-Gromov inequality, Math. Z., Vol. 289, (2018), no. 3-4, pp. 1191-1197.
40. F. Cavalletti, A. Mondino, Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., Vol. 29, (2018), no. 3, pp. 413-430.
41. F. Galaz-Garcia, M. Kell, A. Mondino, G. Sosa, On quotients of spaces with Ricci curvature bounded below, J. Funct. Anal., Vol. 275, (2018), no. 6, 1368-1446.
42. F. Cavalletti, F. Maggi, A. Mondino, Quantitative isoperimetry a la Levy-Gromov, Communications on Pure and Applied Mathematics, Vol. 72, (2019), no. 8, 1631-1677.
43. N. Ikoma, A. Malchiodi, A. Mondino, Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature, Int. Math. Res. Not. (IMRN) (2018), https://doi.org/10.1093/imrn/rny203
44. A. Lerario, A. Mondino, Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics, Transactions of the Amer. Math. Soc. Series B, Vol. 6, 187-214, (May 6, 2019) https://doi.org/10.1090/btran/33.
45. A. Mondino, S. Suhr, An optimal transport formulation of the Einstein equations of general relativity, Journal of the European Math. Society (JEMS), published online (January 2022), DOI 10.4171/JEMS/1188. 62 pages.
46. A. Mondino, D. Semola, Polya-Szego inequality and Dirichlet p-spectral gap for non-smooth spaces with Ricci curvature bounded below, Journal de Mathématiques Pures et Appliquées, Vol. 137, (2020), 238–274.
47. F. Cavalletti, A. Mondino, New formulas for the Laplacian of distance functions and applications, Analysis & PDE, Vol. 13, (2020), 2091–2147.
48. N. De Ponti, A. Mondino, Sharp Cheeger-Buser type inequalities in RCD(K, ∞) spaces, The Journal of Geometric Analysis, Vol. 31 (3), (2021), 2416–2438.
49. A. Mondino, C. Scharrer, Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy, Arch. Rational Mech. Anal., Vol. 236, (2020), 1455–1485.
50. F. Cavalletti, A. Mondino, D. Semola, Quantitative Obata’s Theorem, preprint arXiv:1910.06637, pp. 1-37, (2019). To appear in Analysis & PDE.
51. V. Kapovitch, A.Mondino, On the topology and the boundary of N-dimensional RCD(K,N) spaces, Geometry & Topology, Vol. 25, (2021), 445-495.
52. A. Mondino, M. Vedovato, A Talenti-type comparison theorem for RCD(K,N) spaces and applications, Calc. Var. PDE, Vol. 60, Num. 157, (2021), 43 pp. DOI:10.1007/s00526-021-01971-1.
53. N. De Ponti, A. Mondino, D. Semola, The equality case in Cheeger’s and Buser’s inequalities on RCD spaces, Journ. Funct. Analysis., Volume 281, Issue 3, 1 August 2021, 36 pp. DOI:10.1016/j.jfa.2021.109022
54. A. Mondino, C. Scharrer, A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint, Advances in Calculus of Variations, vol. 16, no. 3, 2023, pp. 529-540. https://doi.org/10.1515/acv-2021-0002.
55. N. De Ponti, A. Mondino, Entropy-Transport distances between unbalanced metric measure spaces, Probab. Theory Relat. Fields (2022). pp. 1–50. https://doi.org/10.1007/s00440-022-01159-4.
56. I. Mondello, A. Mondino, R. Perales, An upper bound on the revised first Betti number and a torus stability result for RCD spaces, Commentarii Mathematici Helvetici (2022). pp. 1–55. DOI 10.4171/CMH/540.
57. A. Mondino, A. Templeton-Browne, Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity, J. Lond. Math. Soc. (2) 106 (2022), no. 3, 1844–1896.
58. B. G. De Luca, N. De Ponti, A. Mondino, A. Tomasiello, Cheeger bounds on spin-2 fields, Journal of High Energy Physics (JHEP), (2021), no. 12, Paper No. 217, 50 pp.
59. M. A. Gunes and A. Mondino, A reverse H ̈older inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces, Proc. Amer. Math. Soc., Vol. 151 (2023), no. 1, 295–311.
60. A. Mondino, D. Semola, Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds, preprint arXiv:2107.12344, (2021). To appear in Memoirs of the American Math. Society. XX+100 pp.
61. A. Mondino and D. Navarro, Moduli spaces of compact RCD(0,N)-structures, Mathematische Annalen, (2022), 38 pp. https://doi.org/10.1007/s00208-022-02493-7.
62. F. Cavalletti and A. Mondino, A review of Lorentzian synthetic theory of timelike Ricci curvature bounds, General Relativity and Gravitation 54 (2022), no. 11, Paper No. 137, 39 pp.
63. E. Brué, A. Mondino, D. Semola, The metric measure boundary of spaces with Ricci curvature bounded below, Geometric and Functional Analysis (GAFA), Vol. 33, 593–636 (2023). https://doi.org/10.1007/s00039-023-00626-x.
64. B. G. De Luca, N. De Ponti, A. Mondino, A. Tomasiello, Gravity from thermodynamics: optimal transport and negative effective dimensions, preprint arXiv:2212.02511, pp. 1–71, (2022). To appear in SciPost Physics.
65. N. Gigli, A. Mondino, D. Semola, On the notion of Laplacian bounds on RCD spaces and applications, preprint arXiv:2302.05474, pp.1–12, (2023). To appear in Proceedings of the Amer. Math. Soc.
PREPUBLICATIONS
66. F. Cavalletti, A. Mondino, Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications, preprint arXiv:2004.08934, pp.1–70, (2020).
67. A. Michelat and A. Mondino, Quantization of the Willmore Energy in Riemannian Manifolds, preprint arXiv:2112.13831, pp. 1–82, (2021).
68. A. Mondino and D. Semola, Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from RCD(K,N) spaces to CAT(0) spaces, preprint arXiv:2202.01590, pp. 1–48, (2022).
69. D. Barilari, A. Mondino, L. Rizzi, Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures, preprint arXiv:2211.07762, pp. 1–148, (2022).
70. B. G. De Luca, N. De Ponti, A. Mondino, A. Tomasiello, Harmonic functions and gravity localization, preprint arXiv:2306.05456, pp. 1–43, (2023).
71. F. Fiorani, A. Mondino, D. Semola, Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces, preprint arXiv:2307.06205, pp. 1–37, (2023).
PROCEEDINGS
72. A. Mondino, The Willmore Functional: a perturbative approach, Online Proceedings of the "International Conference on the Isoperimetric Problem of Queen Dido and its Mathematical Ramifications", (2010).
73. A. Mondino, The Willmore and other Lp-curvature functionals in Riemannian manifolds, MFO Oberwolach Reports, Report Num. 36/2012, DOI:10.4171/OWR/2012/36, Calculus of Variations, 23-26, (2012).
74. A. Mondino, Some new relations between CD(K,N), the dimensional Bakry-Emery condition and the EVI property of gradient flows, MFO Oberwolach Reports, Report Num. 23/2013, DOI:10.4171/OWR/2013/23, Heat Kernels, Stochastic Processes and Functional Inequalities, (2013).
75. A. Mondino, A frame energy for tori immersed in Rm: sharp Willmore-conjecture type lower bound, regularity of critical points and applications, MFO Oberwolach Reports (2013).
76. A. Mondino, PDEs in metric measure spaces and geometric applications, MFO Oberwolach Reports (2013).
77. A. Mondino, Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds, MFO Oberwolach Reports (2015).
78. R. Kusner, A. Mondino, F. Schulze, Willmore Bending Energy on the Space of Surfaces, MSRI Emissary, spring (2016).
79. A. Mondino, On a isoperimetric-isodiametric inequality, MFO Oberwolfach Reports (2016).
80. A. Mondino, Functional inequalities via a 1-dimensional localization method, MFO Oberwolfach Reports (2016), Heat Kernels, Stochastic Processes and Functional Inequalities.
81. N. Ikoma, A. Malchiodi, A. Mondino, Area-constrained Willmore surfaces of small area in Riemannian three-manifolds: an approach via Lyapunov-Schmidt reduction, Regularity and singularity for partial differential equations with conservation laws, pp. 31-50, RIMS Kokyuroku Bessatsu, B63, Res. Inst. Math. Sci. (RIMS), Kyoto, 2017.
Positions
- Tutorial Fellow in Mathematics
- Professor of Mathematics at the Oxford Mathematical Institute
Subjects
- Mathematics
