Welcome to the Home Page of the Research Group in Calculus of Variations and Geometric Measure Theory at Pisa. Look here to know more about us. Please, feel free to download and use all the material you find interesting. If you want to receive regularly the group news, subscribe to our mailing list in the mail section.

If you want to receive an account to insert your preprints, fill-in the account request.

- Geometric Measure Theory in non Euclidean spaces (Luigi Ambrosio) > papers
- Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture (Gianni Dal Maso)
- Analytic Techniques for Geometric and Functional Inequalities (Nicola Fusco)
- Analysis of Optimal Sets and Optimal Constants: Old Questions and New Results (Aldo Pratelli)
- Mathematics for Shape Memory Technologies in Biomechanics (Ulisse Stefanelli)
- Geometry of Metric Groups (Enrico Le Donne) > papers
- Variational approach to the regularity of the free boundaries (Bozhidar Velichkov)

- PhD position, Marie Curie Network TraDE-Opt, University of Graz (deadline: 17 Mar 2021)
- Post-doc at the University of Firenze (deadline: 30 Mar 2021)
- 5-10 Postdoctoral and 1-2 Ph.D. student positions at Jyväskylä (deadline: 31 Mar 2021)
- 2-years postdoc position in Analysis at Bocconi University, Milan (deadline: 31 Mar 2021)
- PhD position in spectral theory of differential operators, Oldenburg (deadline: 7 May 2021)
- Recruitment of Shing-Tung Yau Center of Southeast University (SEU-Yau Center) Nanjing, China (deadline: 11 Feb 2022)
- Recruitment of the Nanjing Center for Applied Mathematics（NCAM） Nanjing, China (deadline: 11 Feb 2022)

- 9 Mar 2021:
**D. Vittone:***Differentiability of intrinsic Lipschitz graphs in Carnot groups* - 18 Mar 2021:
**I. Lucardesi:***Shape optimization in the class of bodies of constant width.* - 15 Apr 2021:
**R. Scala:***Nonlocality features of the area functional and the Plateau problem*

- 18 Nov 2020 - 15 Sep 2021: NCTS International Geometric Measure Theory Seminar
- 22 - 23 Mar 2021: Nonlinear Meeting 2021 Online
- 29 Mar - 2 Apr 2021: Research School "Shape Optimization, Spectral Geometry and Calculus of Variations" CIRM, Luminy, France
- 8 - 8 Apr 2021: Online Poster Session "Young Researchers in PDE and Geometric Analysis" Online
- 12 - 16 Apr 2021: Optimization of shape and material properties: advanced mathematical methods and 3D printing CISM, Udine
- 12 - 16 Apr 2021: Hausdorff School: “Diffusive Systems” Bonn
- 19 - 21 May 2021: ''Workshop on $L^\infty$ and constrained variational problems''. Online
- 7 - 11 Jun 2021: Workshop "Variational methods and applications" Centro De Giorgi, Pisa
- 21 - 25 Jun 2021: Tenth Summer School in Analysis and Applied Mathematics Dipartimento di Matematica - Sapienza, Università di Roma
- 28 Jun - 2 Jul 2021: Como Lake School Mathematical Models for Bio-Medical Sciences moved to 2021 Villa del Grumello, Como
- 5 - 9 Jul 2021: Special session "Sub-Riemannian Geometry and Interactions", within the AMS-SMF-EMS Joint International Meeting in Grenoble, 2021 Grenoble
- 1 - 31 Aug 2021: Jyväskylä Summer School Jyväskylä, Finland
- 20 Sep - 17 Dec 2021: Distributed Solutions to Complex Societal Problems University of Chicago, USA
- 6 - 8 Apr 2022: Probability, Analysis and Dynamics '22 Bristol
- 13 - 17 Jun 2022: Shape Optimization, related topics and applications Roskoff Biological center, Bretagne
- 19 - 23 Sep 2022: Shape Optimisation and Geometric Spectral Theory ICMS, Edinburgh

- G. Bellettini - A. Elshorbagy - R. Scala (Preprint)

The $L^1$-relaxed area of the graph of the vortex map (2021) - N. Fusco - M. Morini (Submitted Paper)

Total positive curvature and the equality case in the relative isoperimetric inequality outside convex domains (2021) - N. De Nitti - F. Hounkpe - S. Schulz (Submitted Paper)

On Liouville-type theorems for the 2D stationary MHD equations (2021) - G. Di Fratta - A. Fiorenza (Preprint)

A unified divergent approach to Hardy-Poincaré inequalities in classical and variable Sobolev Spaces (2021) - I. Y. Violo (preprint)

A remark on two notions of flatness for sets in the Euclidean space (2021) - L. De Luca - A. Kubin - M. Ponsiglione (Preprint)

Convergence of supercritical fractional flows to the mean curvature flow (2021) - D. Bucur - I. Fragalà (preprint)

Rigidity for measurable sets (2021) - Y. Brenier - W. Gangbo - G. Savaré - M. Westdickenberg (preprint)

Sticky particle dynamics with interactions (2012) - J. Dolbeault - B. Nazaret - G. Savaré (preprint)

A new class of transport distances (2008) - G. Savaré (preprint)

Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces (2013) - G. Savaré - G. Toscani (preprint)

The concavity of Rènyi entropy power (2012) - M. Liero - A. Mielke - G. Savaré (preprint)

Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves (2015) - M. Liero - A. Mielke - G. Savaré (preprint)

Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures (2015) - G. Savaré (preprint)

Sobolev spaces in extended metric-measure spaces (2019) - E. Pasqualetto - T. Schultz (preprint)

Ultralimits of pointed metric measure spaces (2021) - J. F. Babadjian - F. Iurlano - F. Rindler (preprint)

Shape optimization of light structures and the vanishing mass conjecture (2021)

- A. Maione - A. M. Salort - E. Vecchi (Accepted Paper:
*Asymptotic Analysis*)

Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces (2021) - M. Capolli - A. Maione - A. M. Salort - E. Vecchi (
*The Journal of Geometric Analysis*)

Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups (2021) - A. Braides - V. Chiadò Piat - L. D'Elia (
*Nonlinear Analysis*)

An extension theorem from connected sets and homogenization of non-local functionals (2021) - C. De Lellis - M. Focardi - S. Ghinassi (Accepted Paper:
*J. Math. Pures Appl.*)

Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan (2020) - G. Scilla - F. Solombrino (
*NoDEA Nonlinear Differential Equations Appl.*)

Non-local approximation of the Griffith functional (2021) - E. Paolini - V. M. Tortorelli (
*Calc. Var.*)

The quadruple planar bubble enclosing equal areas is symmetric (2020) - H. Kröner - M. Novaga - P. Pozzi (Accepted Paper:
*Milan J. Math.*)

Anisotropic curvature flow of immersed networks (2020) - I. Mazari (Preprint)

Quantitative estimates for parabolic optimal control problems under L∞ and L1 constraints in the ball: Quantifying parabolic isoperimetric inequalities (2021) - A. Cesaroni - V. Pagliari (Accepted Paper:
*Discrete & Continuous Dynamical Systems - A*)

Convergence of nonlocal geometric flows to anisotropic mean curvature motion (2021) - F. Cavalletti - F. Santarcangelo (
*J. Funct. Anal.*)

Isoperimetric inequality under Measure-Contraction property (2018) - A. Akdemir - F. Cavalletti - A. Colinet - R. J. McCann - F. Santarcangelo (Accepted Paper:
*Trans. Amer. Math. Soc.*)

Independence of synthetic Curvature Dimension conditions on transport distance exponent (2020) - F. Cavalletti - N. Gigli - F. Santarcangelo (Accepted Paper:
*Annales de la faculté des sciences de Toulouse*)

Displacement convexity of Entropy and the distance cost Optimal Transportation (2020) - F. Cavalletti - E. Milman (Accepted Paper:
*Inventiones Math.*)

The Globalization Theorem for the Curvature Dimension Condition (2016) - B. Bulanyi - A. Lemenant (Reviewed version)

Regularity for the planar optimal $p$-compliance problem (2021)