A. Mondino:
Some results about the existence of critical points for the Willmore functional
Math. Z. Vol. 266, N. 3, p. 583--622, 2010
A. Mondino:
Existence of Integral m-Varifolds minimizing $\int |A|^p$ and $\int |H|^p$, p>m, in Riemannian Manifolds
Calc. Var. PDE 2010
A. Mondino, T. Rivière:
Immersed Spheres of Finite Total Curvature into Manifolds
Advances in Calc. Var. (Accepted Paper) p. 33, 2011
A. Mondino:
The conformal Willmore Functional: a perturbative approach
Journal of Geometric Analysis 2011
E. Kuwert, A. Mondino, J. Schygulla:
Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds
Math. Annalen (Accepted Paper) 2011
A. Mondino:
The Willmore functional and other $L^p$ curvature functionals in Riemannian manifolds
(Phd Thesis) 2011
A. Mondino:
The Willmore and other $L^p$-curvature functionals in Riemannian manifolds
Oberwolfach Reports Vol. 36/2012, p. 23-26, 2012
L. Ambrosio, N. Gigli, A. Mondino, T. Rajala:
Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
Transactions of the AMS (Accepted Paper) 2012
A. Mondino, T. Rivière:
Willmore Spheres in Compact Riemannian Manifolds
Advances in Math. p. 58, 2012
A. Mondino, J. Schygulla:
Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds
Annales IHP-Anal. Non Lin. (Accepted Paper) p. 19, 2012
N. Gigli, A. Mondino:
A PDE approach to nonlinear potential theory in metric measure spaces
Journal de Math. Pures et Appl. 2012
A. Mondino, S. Nardulli:
Existence of isoperimetric regions in non-compact Riemannian manifolds under Ricci or scalar curvature conditions
Communications in Analysis and Geometry p. 17, 2012
N. Gigli, A. Mondino, T. Rajala:
Euclidean spaces as weak tangents of infinitesimally Hilbertian metric measure spaces with Ricci curvature bounded below
J. Reine Angew. Math. (Accepted Paper) 2013
L. G. A. Keller, A. Mondino, T. Rivière:
Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint
Arch. Rat. Mech. Anal. (Accepted Paper) 2013
N. Garofalo, A. Mondino:
Li-Yau and Harnack type inequalities in $RCD^*(K,N)$ metric measure spaces
Nonlinear Analysis TMA (Accepted Paper) 2013
A. Mondino:
A new notion of angle between three points in a metric space
Crelle's Journal (Accepted Paper) 2013
A. Carlotto, A. Mondino:
Existence of generalized totally umbilic 2-spheres in perturbed 3-spheres
Int. Math. Res. Not. (Accepted Paper) 2013
A. Mondino, H. T. Nguyen:
A Gap Theorem for Willmore Tori and an application to the Willmore Flow
(Nonlinear Analysis: Theory Methods & Applications) 2013
P. Laurain, A. Mondino:
Concentration of small Willmore spheres in Riemannian 3-manifolds
Analysis and PDEs 2013
N. Gigli, A. Mondino, G. Savaré:
Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
Proceedings of the London Mathematical Society (Accepted Paper) 2013
A. Mondino, T. Rivière:
A frame energy for immersed tori and applications to regular homotopy classes
Journal of Differential Geometry (Accepted Paper) 2013
L. Ambrosio, A. Mondino, G. Savaré:
On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces
Journal of Geometric Analysis (Accepted Paper) 2014
N. Ikoma, A. Malchiodi, A. Mondino:
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds II: Morse Theory
(American Journal of Mathematics) 2014
A. Mondino, A. Naber:
Structure Theory of Metric-Measure Spaces with Lower Ricci Curvature Bounds
Journ. European Math Soc. (JEMS) (Accepted Paper) 2014
N. Ikoma, A. Malchiodi, A. Mondino:
Embedded area-constrained Willmore tori of small area in Riemannian three-manifolds I: Minimization
(Proceedings of the London Math. Soc.) 2014
F. Cavalletti, A. Mondino:
Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
Geom. Topol. () 2015
F. Cavalletti, A. Mondino:
Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds
Invent. Math. (Accepted Paper) 2015
L. Ambrosio, A. Mondino, G. Savaré:
Nonlinear diffusion equations and curvature conditions in metric measure spaces
Memoirs Amer. Math. Soc. (Accepted Paper) 2015
A. Mondino, H. T. Nguyen:
Global conformal invariants of submanifolds
Annales de l'Institut Fourier (Accepted Paper) 2015
A. Lerario, A. Mondino:
Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics
Transactions of the American Math Society, Series B. (Accepted Paper) 2015
A. Carlotto, A. Mondino:
A non-existence result for minimal catenoids in asymptotically flat spaces
(Journal of London Math. Society) 2016
A. Mondino, G. Wei:
On the universal cover and the fundamental group of an $RCD^*(K,N)$-space
(Journal für die reine und angewandte mathematik) 2016
L. Ambrosio, A. Mondino:
Gaussian-type Isoperimetric Inequalities in $RCD(K,\infty)$ probability spaces for positive $K$
Rend. Lincei Mat. Appl. Vol. 27, p. 497514, 2016
F. Cavalletti, A. Mondino:
Optimal maps in essentially non-branching spaces
Commun. Contemp. Math. (Accepted Paper) 2016
F. Cavalletti, A. Mondino:
Measure rigidity of Ricci curvature lower bounds
Advances in Math. (accepted) Vol. 286, 2016
M. Kell, A. Mondino:
On the volume measure of non-smooth spaces with Ricci curvature bounded below
Annali SNS (Accepted Paper) 2016
F. Cavalletti, A. Mondino:
Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
Rend. Lincei. Mat. Appl. (Accepted Paper) 2016
A. Mondino, E. Spadaro:
On a isoperimetric-isodiametric inequality
(Analysis & PDE) 2016
F. Cavalletti, F. Maggi, A. Mondino:
Rigidity for critical points in the Levy-Gromov inequality
Math. Zeit p. 5, 2016
C. Ketterer, A. Mondino:
Sectional and intermediate Ricci curvature lower bounds via Optimal Transport
Advances in Mathematics (Accepted Paper) 2016
F. Cavalletti, A. Mondino:
Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds
Intern. Math. Res. Not. (Accepted Paper) 2017
F. Cavalletti, F. Maggi, A. Mondino:
Quantitative isoperimetry à la Levy-Gromov
Comm. Pure and Applied Math. (Accepted Paper) 2017
B. Han, A. Mondino:
Angles between curves in metric measure spaces
Analysis and Geometry in Metric Spaces Vol. 5, N. 1, p. 47--68, 2017
F. Galaz-Garcia, M. Kell, A. Mondino, G. Sosa:
On quotients of spaces with Ricci curvature bounded below
Journal of Functional Analysis (Accepted Paper) 2017
N. Ikoma, A. Malchiodi, A. Mondino:
Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
Intern. Math. Res. Not. (IMRN) (Accepted Paper) 2018
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 2018
F. Cavalletti, A. Mondino:
New formulas for the Laplacian of distance functions and applications
Analysis and PDE (Accepted Paper) 2018
A. Mondino, S. Suhr:
An optimal transport formulation of the Einstein equations of general relativity
Journal of the European Math. Society (JEMS) (Accepted Paper) p. 60, 2018
V. Kapovitch, A. Mondino:
On the topology and the boundary of $N$-dimensional $RCD(K,N)$ spaces
Geometry & Topology (Accepted Paper) 2019
A. Mondino, C. Scharrer:
Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy
Archive for Rational Mechanics and Analysis 2020
A. Mondino, C. Scharrer:
A strict inequality for the minimisation of the Willmore functional under isoperimetric constraint
Advances in Calculus of Variations (Accepted Paper) 2020
N. De Ponti, A. Mondino:
Sharp Cheeger-Buser type inequalities in $RCD(K,\infty)$ spaces
The Journal of Geometric Analysis 2020
A. Mondino, M. Vedovato:
A Talenti-type comparison theorem for $\mathrm{RCD}(K,N)$ spaces and applications
Calc. Var. PDE (Accepted Paper) 2020
N. De Ponti, A. Mondino:
Entropy-Transport distances between unbalanced metric measure spaces
Probability Theory and Related Fields (Accepted Paper) 2020
F. Cavalletti, A. Mondino:
Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications
Cambridge Journal of Mathematics (Accepted Paper) 2020
A. Michelat, A. Mondino:
Quantization of the Willmore Energy in Riemannian Manifolds
(Preprint) 2021
G. B. De Luca, N. De Ponti, A. Mondino, A. Tomasiello:
Cheeger bounds on spin-two fields
Journal of High Energy Physics 2021
M. A. Gunes, A. Mondino:
A reverse Hölder inequality for first eigenfunctions of the Dirichlet Laplacian on RCD(K,N) spaces
Proc. Amer. Math. Soc. (Accepted Paper) 2021
N. De Ponti, A. Mondino, D. Semola:
The equality case in Cheeger's and Buser's inequalities on $ \mathsf{RCD}$ spaces
Journal of Functional Analysis Vol. 281, N. 3, 2021
A. Mondino, A. Templeton-Browne:
Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity
Journal of the London Math. Society (Accepted Paper) p. 39, 2021
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 (Accepted Paper) 2021
A. Mondino, D. Semola:
Weak Laplacian bounds and minimal boundaries in non-smooth spaces with Ricci curvature lower bounds
Memoirs of the American Mathematical Society (Accepted Paper) 2021
F. Cavalletti, A. Mondino:
A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
General Relativity and Gravitation 2022
E. Bruè, A. Mondino, D. Semola:
The metric measure boundary of spaces with Ricci curvature bounded below
GAFA p. 32, 2022
A. Mondino, D. Navarro:
Moduli spaces of compact RCD(0,N)-structures
Math. Annalen (Accepted Paper) 2022
G. B. De Luca, N. De Ponti, A. Mondino, A. Tomasiello:
Gravity from thermodynamics: optimal transport and negative effective dimensions
SciPost Physics (Accepted Paper) 2022
A. Mondino, D. Semola:
Lipschitz continuity and Bochner-Eells-Sampson inequality for harmonic maps from $\mathrm{RCD}(K,N)$ spaces to $\mathrm{CAT}(0)$ spaces
American Journal of Mathematics (Accepted Paper) p. 48, 2022
N. Gigli, A. Mondino, D. Semola:
On the notion of Laplacian bounds on $\mathrm{RCD}$ spaces and applications
Proc. Amer. Math. Soc. (Accepted Paper) p. 12, 2023
F. Fiorani, A. Mondino, D. Semola:
Monotonicity formula and stratification of the singular set of perimeter minimizers in RCD spaces
(Preprint) 2023
F. Cavalletti, A. Mondino, D. Semola:
Quantitative Obata's Theorem
Analysis & PDE Vol. 16, N. 6, p. 13891431, 2023
G. B. De Luca, N. De Ponti, A. Mondino, A. Tomasiello:
Harmonic functions and gravity localization
The Journal of High Energy Physics (Accepted Paper) 2023
A. Mondino, V. Ryborz:
On the equivalence of distributional and synthetic Ricci curvature lower bounds
(Preprint) 2024
D. Barilari, A. Mondino, L. Rizzi:
Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures
Memoirs of the AMS (Accepted Paper) 2024
F. Cavalletti, A. Mondino:
A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds
(Preprint) 2024
A. Cucinotta, A. Mondino:
Half Space Property in RCD(0,N) spaces
(Preprint) 2024