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
A. Mondino:
The Willmore functional and other $L^p$ curvature functionals in Riemannian manifolds
(Phd Thesis) 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 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 (Accepted Paper) 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
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
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, 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
A. Lerario, A. Mondino:
Homotopy properties of horizontal loop spaces and applications to closed sub-riemannian geodesics
(Submitted Paper) 2015
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
F. Cavalletti, A. Mondino:
Measure rigidity of Ricci curvature lower bounds
Advances in Math. (accepted) Vol. 286, 2016
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
A. Mondino, E. Spadaro:
On a isoperimetric-isodiametric inequality
(Analysis & PDE) 2016
M. Kell, A. Mondino:
On the volume measure of non-smooth spaces with Ricci curvature bounded below
Annali SNS (Accepted Paper) 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:
Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds
Rend. Lincei. Mat. Appl. (Accepted Paper) 2016
F. Cavalletti, F. Maggi, A. Mondino:
Rigidity for critical points in the Levy-Gromov inequality
Math. Zeit p. 5, 2016
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. Cavalletti, A. Mondino:
Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds
Intern. Math. Res. Not. (Accepted Paper) 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
F. Cavalletti, F. Maggi, A. Mondino:
Quantitative isoperimetry à la Levy-Gromov
Comm. Pure and Applied Math. (Accepted Paper) 2017
F. Cavalletti, A. Mondino:
New formulas for the Laplacian of distance functions and applications
(Preprint) 2018
N. Ikoma, A. Malchiodi, A. Mondino:
Foliation by area-constrained Willmore spheres near a non-degenerate critical point of the scalar curvature
(Submitted Paper) 2018
A. Mondino, D. Semola:
Polya-Szego inequality and Dirichlet $p$-spectral gap for non-smooth spaces with Ricci curvature bounded below
(Preprint) 2018