[mondino]

Associate Professor, University of Oxford

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

- G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello (Preprint)

Cheeger bounds on spin-two fields (2021) - M. A. Gunes - A. Mondino (Submitted Paper)

A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces (2021) - I. Mondello - A. Mondino - R. Perales (Submitted Paper)

An upper bound on the revised first Betti number and a torus stability result for RCD 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 (Submitted Paper)

Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity (2021) - A. Mondino - D. Semola (Preprint)

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) - N. De Ponti - A. Mondino (Submitted Paper)

Entropy-Transport distances between unbalanced metric measure spaces (2020) - F. Cavalletti - A. Mondino (Preprint)

Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications (2020) - A. Mondino - M. Vedovato (Accepted Paper:
*Calc. Var. PDE*)

A Talenti-type comparison theorem for $\mathrm{RCD}(K,N)$ spaces and applications (2020) - F. Cavalletti - A. Mondino - D. Semola (Preprint)

Quantitative Obata's Theorem (2019) - 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) - F. Cavalletti - A. Mondino (accepted:
*Advances in Math.*)

Measure rigidity of Ricci curvature lower bounds (2016) - 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) - 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)

*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

*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

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