Full Professor, University of Oxford

Email: Andrea.Mondino AT maths.ox.ac.uk

Available papers (81):

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• F. Cavalletti - A. Mondino (Preprint)
  A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds (2025)
• A. Mondino - V. Ryborz (Preprint)
  On the equivalence of distributional and synthetic Ricci curvature lower bounds (2024)
• D. Barilari - A. Mondino - L. Rizzi (Accepted Paper: Memoirs of the AMS)
  Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures (2024)
• N. Gigli - A. Mondino - D. Semola (Proc. Amer. Math. Soc.)
  On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications (2024)
• S. Honda - A. Mondino (Submitted Paper)
  Gap phenomena under curvature restrictions (2024)
• S. Honda - A. Mondino (Archiv Der Mathematik)
  Poincar\'e inequality for one forms on four manifolds with bounded Ricci curvature (2024)
• A. Cucinotta - A. Mondino (Preprint)
  Half Space Property in RCD(0,N) spaces (2024)
• A. Cucinotta - A. Mondino (Preprint)
  A splitting theorem for manifolds with a convex boundary component and applications to the half-space property (2024)
• F. Cavalletti - D. Manini - A. Mondino (preprint)
  Optimal transport on null hypersurfaces and the null energy condition (2024)
• A. Kristály - A. Mondino (Submitted Paper)
  Principal frequency of clamped plates on RCD(0,N) spaces: sharpness, rigidity and stability (2024)
• G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello (Journal of High Energy Physics)
  Can you hear the Planck mass? (2024)
• F. Cavalletti - A. Mondino - D. Semola (Analysis & PDE)
  Quantitative Obata's Theorem (2023)
• E. Bruè - A. Mondino - D. Semola (Geom. Funct. Anal.)
  The metric measure boundary of spaces with Ricci curvature bounded below (2023)
• F. Fiorani - A. Mondino - D. Semola (Accepted Paper: Commentarii Mathematici Helvetici)
  Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces (2023)
• G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello (Accepted Paper: The Journal of High Energy Physics)
  Harmonic functions and gravity localization (2023)
• F. Cavalletti - A. Mondino (General Relativity and Gravitation)
  A review of Lorentzian synthetic theory of timelike Ricci curvature bounds (2022)
• A. Mondino - D. Navarro (Accepted Paper: Math. Annalen)
  Moduli spaces of compact RCD(0,N)-structures (2022)
• G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello (Accepted Paper: SciPost Physics)
  Gravity from thermodynamics: optimal transport and negative effective dimensions (2022)
• A. Mondino - D. Semola (Accepted Paper: American Journal of Mathematics)
  Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from $\mathrm{RCD}(K,N)$ spaces to $\mathrm{CAT}(0)$ spaces (2022)
• A. Michelat - A. Mondino (Preprint)
  Quantization of the Willmore Energy in Riemannian Manifolds (2021)
• G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello (Journal of High Energy Physics)
  Cheeger bounds on spin-two fields (2021)
• M. A. Gunes - A. Mondino (Accepted Paper: Proc. Amer. Math. Soc.)
  A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces (2021)
• N. De Ponti - A. Mondino - D. Semola (Journal of Functional Analysis)
  The equality case in Cheeger's and Buser's inequalities on $ \mathsf{RCD}$ spaces (2021)
• A. Mondino - A. Templeton-Browne (Accepted Paper: Journal of the London Math. Society)
  Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity (2021)
• I. Mondello - A. Mondino - R. Perales (Accepted Paper: Commentarii Mathematici Helvetici)
  An upper bound on the revised first Betti number and a torus stability result for RCD spaces (2021)
• A. Mondino - D. Semola (Accepted Paper: Memoirs of the American Mathematical Society)
  Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds (2021)
• A. Mondino - C. Scharrer (Archive for Rational Mechanics and Analysis)
  Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy (2020)
• A. Mondino - C. Scharrer (Accepted Paper: Advances in Calculus of Variations)
  A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint (2020)
• N. De Ponti - A. Mondino (The Journal of Geometric Analysis)
  Sharp Cheeger-Buser type inequalities in $RCD(K,\infty)$ spaces (2020)
• A. Mondino - M. Vedovato (Accepted Paper: Calc. Var. PDE)
  A Talenti-type comparison theorem for $\mathrm{RCD}(K,N)$ spaces and applications (2020)
• N. De Ponti - A. Mondino (Accepted Paper: Probability Theory and Related Fields)
  Entropy-Transport distances between unbalanced metric measure spaces (2020)
• F. Cavalletti - A. Mondino (Accepted Paper: Cambridge Journal of Mathematics)
  Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications (2020)
• V. Kapovitch - A. Mondino (Accepted Paper: Geometry & Topology)
  On the topology and the boundary of $N$-dimensional $RCD(K,N)$ spaces (2019)
• N. Ikoma - A. Malchiodi - A. Mondino (Accepted Paper: Intern. Math. Res. Not. (IMRN))
  Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature (2018)
• A. Mondino - D. Semola (Journal de Mathématiques Pures et Appliquées)
  Polya-Szego inequality and Dirichlet $p$-spectral gap for non-smooth spaces with Ricci curvature bounded below (2018)
• F. Cavalletti - A. Mondino (Accepted Paper: Analysis and PDE)
  New formulas for the Laplacian of distance functions and applications (2018)
• A. Mondino - S. Suhr (Accepted Paper: Journal of the European Math. Society (JEMS))
  An optimal transport formulation of the Einstein equations of general relativity (2018)
• F. Cavalletti - A. Mondino (Accepted Paper: Intern. Math. Res. Not.)
  Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds (2017)
• F. Cavalletti - F. Maggi - A. Mondino (Accepted Paper: Comm. Pure and Applied Math.)
  Quantitative isoperimetry à la Levy-Gromov (2017)
• B. Han - A. Mondino (Analysis and Geometry in Metric Spaces)
  Angles between curves in metric measure spaces (2017)
• F. Galaz-Garcia - M. Kell - A. Mondino - G. Sosa (Accepted Paper: Journal of Functional Analysis)
  On quotients of spaces with Ricci curvature bounded below (2017)
• A. Carlotto - A. Mondino (Journal of London Math. Society)
  A non-existence result for minimal catenoids in asymptotically flat spaces (2016)
• A. Mondino - G. Wei (Journal für die reine und angewandte mathematik)
  On the universal cover and the fundamental group of an $RCD^*(K,N)$-space (2016)
• L. Ambrosio - A. Mondino (Rend. Lincei Mat. Appl.)
  Gaussian-type Isoperimetric Inequalities in $RCD(K,\infty)$ probability spaces for positive $K$ (2016)
• F. Cavalletti - A. Mondino (Accepted Paper: Commun. Contemp. Math.)
  Optimal maps in essentially non-branching spaces (2016)
• F. Cavalletti - A. Mondino (accepted: Advances in Math.)
  Measure rigidity of Ricci curvature lower bounds (2016)
• M. Kell - A. Mondino (Accepted Paper: Annali SNS)
  On the volume measure of non-smooth spaces with Ricci curvature bounded below (2016)
• F. Cavalletti - A. Mondino (Accepted Paper: Rend. Lincei. Mat. Appl.)
  Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds (2016)
• A. Mondino - E. Spadaro (Analysis & PDE)
  On a isoperimetric-isodiametric inequality (2016)
• F. Cavalletti - F. Maggi - A. Mondino (Math. Zeit)
  Rigidity for critical points in the Levy-Gromov inequality (2016)
• C. Ketterer - A. Mondino (Accepted Paper: Advances in Mathematics)
  Sectional and intermediate Ricci curvature lower bounds via Optimal Transport (2016)
• F. Cavalletti - A. Mondino (Geom. Topol.)
  Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (2015)
• F. Cavalletti - A. Mondino (Accepted Paper: Invent. Math. )
  Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (2015)
• L. Ambrosio - A. Mondino - G. Savaré (Accepted Paper: Memoirs Amer. Math. Soc.)
  Nonlinear diffusion equations and curvature conditions in metric measure spaces (2015)
• A. Mondino - H. T. Nguyen (Accepted Paper: Annales de l'Institut Fourier)
  Global conformal invariants of submanifolds (2015)
• A. Lerario - A. Mondino (Accepted Paper: Transactions of the American Math Society, Series B.)
  Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics (2015)
• L. Ambrosio - A. Mondino - G. Savaré (Accepted Paper: Journal of Geometric Analysis)
  On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces (2014)
• N. Ikoma - A. Malchiodi - A. Mondino (American Journal of Mathematics)
  Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II: Morse Theory (2014)
• A. Mondino - A. Naber (Accepted Paper: Journ. European Math Soc. (JEMS))
  Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds (2014)
• N. Ikoma - A. Malchiodi - A. Mondino (Proceedings of the London Math. Soc.)
  Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization (2014)
• N. Gigli - A. Mondino - T. Rajala (Accepted Paper: J. Reine Angew. Math.)
  Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below (2013)
• L. G. A. Keller - A. Mondino - T. Rivière (Accepted Paper: Arch. Rat. Mech. Anal.)
  Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint (2013)
• N. Garofalo - A. Mondino (Accepted Paper: Nonlinear Analysis TMA)
  Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces (2013)
• A. Mondino (Accepted Paper: Crelle's Journal)
  A new notion of angle between three points in a metric space (2013)
• A. Carlotto - A. Mondino (Accepted Paper: Int. Math. Res. Not.)
  Existence of generalized totally umbilic 2-spheres in perturbed 3-spheres (2013)
• A. Mondino - H. T. Nguyen (Nonlinear Analysis: Theory Methods & Applications)
  A Gap Theorem for Willmore Tori and an application to the Willmore Flow (2013)
• P. Laurain - A. Mondino (Analysis and PDEs)
  Concentration of small Willmore spheres in Riemannian 3-manifolds (2013)
• N. Gigli - A. Mondino - G. Savaré (Accepted Paper: Proceedings of the London Mathematical Society)
  Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows (2013)
• A. Mondino - T. Rivière (Accepted Paper: Journal of Differential Geometry)
  A frame energy for immersed tori and applications to regular homotopy classes (2013)
• A. Mondino (Oberwolfach Reports)
  The Willmore and other $L^p$-curvature functionals in Riemannian manifolds (2012)
• L. Ambrosio - N. Gigli - A. Mondino - T. Rajala (Accepted Paper: Transactions of the AMS)
  Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure (2012)
• A. Mondino - T. Rivière (Advances in Math.)
  Willmore Spheres in Compact Riemannian Manifolds (2012)
• A. Mondino - J. Schygulla (Accepted Paper: Annales IHP-Anal. Non Lin.)
  Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds (2012)
• N. Gigli - A. Mondino (Journal de Math. Pures et Appl.)
  A PDE approach to nonlinear potential theory in metric measure spaces (2012)
• A. Mondino - S. Nardulli (Communications in Analysis and Geometry)
  Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions (2012)
• A. Mondino - T. Rivière (Accepted Paper: Advances in Calc. Var.)
  Immersed Spheres of Finite Total Curvature into Manifolds (2011)
• A. Mondino (Journal of Geometric Analysis)
  The conformal Willmore Functional: a perturbative approach (2011)
• E. Kuwert - A. Mondino - J. Schygulla (Accepted Paper: Math. Annalen)
  Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds (2011)
• A. Mondino (Phd Thesis)
  The Willmore functional and other $L^p$ curvature functionals in Riemannian manifolds (2011)
• A. Mondino (Math. Z.)
  Some results about the existence of critical points for the Willmore functional (2010)
• A. Mondino (Calc. Var. PDE)
  Existence of Integral m-Varifolds minimizing $\int |A|^p$ and $\int |H|^p$, p>m, in Riemannian Manifolds (2010)

Seminars:

• 30 mar 2021: Optimal transport and quantitative geometric inequalities
• 19 jun 2014: Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint
• 30 jan 2013: A new notion of angle between three points in a metric space
• 23 nov 2011: The Willmore and other $L^2$ curvature functionals in Riemannian manifolds

Speaker:

• 12 sep 2024 - 13 sep 2024: DIFFERENTIAL EVOLUTIVE PROBLEMS IN SPACES WITH SINGULARITIES
• 21 may 2024 - 24 may 2024: Workshop: Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension
• 12 jun 2023 - 16 jun 2023: Calculus of Variations and Geometric Measure Theory
• 9 sep 2019 - 13 sep 2019: Geometric Analysis, Submanifolds, and Geometry of PDE's
• 24 jun 2019 - 28 jun 2019: 11th School on Analysis and Geometry in Metric Spaces
• 12 nov 2018 - 16 nov 2018: Optimal Transport and Applications
• 27 oct 2014 - 31 oct 2014: ERC Workshop on Optimal Transportation and Applications

Organizer:

• 1 apr 2019 - 5 apr 2019: Optimal Transport and Geometric Analysis