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)

- 4 Postdoc and 12 PhD positions in the research group "Symplectic structures in geometry, algebra and dynamics" (deadline: 31 Jan 2021)
- Postdoc in varie aree - Trento (deadline: 1 Feb 2021)
- Research contract in Lisbon (deadline: 11 Feb 2021)
- Recruitment of the Nanjing Center for Applied Mathematics（NCAM） Nanjing, China (deadline: 11 Feb 2021)
- MathInParis2020 - Doctoral Training in Mathematical Sciences in Paris (deadline: 13 Feb 2021)
- 2-years postdoc position in Analysis at TU Munich (deadline: 28 Feb 2021)
- PhD student position at University of Groningen (deadline: 28 Feb 2021)
- Postdoctoral position at WWU Münster (Germany) (deadline: 15 Mar 2021)

- 26 Jan 2021:
**F. Maggi:***Soap films and capillarity theory* - 28 Jan 2021:
**E. Serra:***NLS ground states on metric trees: existence results and open questions*

- 18 Nov 2020 - 15 Sep 2021: NCTS International Geometric Measure Theory Seminar
- 22 - 26 Feb 2021: (Virtual) Winterschool on Analysis and Applied Mathematics Online
- 29 Mar - 2 Apr 2021: Research School "Shape Optimization, Spectral Geometry and Calculus of Variations" CIRM, Luminy, France
- 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

- C. Goodrich - G. Scilla - B. Stroffolini (Submitted Paper)

Partial Hölder continuity for minimizers of discontinuous quasiconvex integrals with VMO coefficients and general growth (2021) - D. Campbell - A. Kauranen - E. Radici (Submitted Paper)

Classification of Strict limits of planar BV homeomorphisms (2021) - E. Cinti - F. Glaudo - A. Pratelli - X. Ros-Oton - J. Serra (Preprint)

Sharp quantitative stability for isoperimetric inequalities with homogeneous weights (2020) - L. Benatti - M. Fogagnolo - L. Mazzieri (preprint)

Minkowski Inequality on Asymptotically Conical manifolds (2021) - E. Marconi (Preprint)

Differentiability properties of the flow of 2d autonomous vector fields (2021) - G. Dal Maso - R. Toader (Submitted Paper)

On the pure jump nature of crack growth for a class of pressure-sensitive elasto-plastic materials (2020) - G. Catino (Preprint)

Metrics of constant negative scalar-Weyl curvature (2021) - F. Cagnetti - G. Dal Maso - L. Scardia - C. I. Zeppieri (Submitted Paper)

A global method for deterministic and stochastic homogenisation in BV (2021) - L. Briani - G. Buttazzo - F. Prinari (Submitted Paper)

A shape optimization problem on planar sets with prescribed topology (2021) - N. Gigli - I. Y. Violo (preprint)

Monotonicity formulas for harmonic functions in ${\rm RCD}(0,N)$ spaces (2021) - P. D. Lamberti - I. Y. Violo (
*Math. Nachr.*)

On Stein's extension operator preserving Sobolev-Morrey spaces (2018) - W. Borrelli - P. Briet - D. Krejcirik - T. Ourmieres-Bonafos (Submitted Paper)

Spectral properties of relativistic quantum waveguides (2021) - W. Borrelli - R. Carlone (Proceedings)

Bifurcating standing waves for effective equations in gapped honeycomb structures (2021) - C. Mantegazza - M. Pozzetta (Submitted Paper)

Asymptotic convergence of evolving hypersurfaces (2021) - M. Pozzetta (Ph.D. Thesis)

Willmore-type Energies of Curves and Surfaces (2020) - J. Lira - R. Mazzeo - A. Pluda - M. Saez (Preprint)

Short-time existence for the network flow (2021) - B. Bulanyi (Submitted Paper)

On the importance of the connectedness assumption in the statement of the optimal $p$-compliance problem (2021) - B. Bulanyi (Preprint)

Partial regularity for the optimal $p$-compliance problem with length penalization (2021) - T. Moisala - E. Pasqualetto (preprint)

Direct limits of infinite-dimensional Carnot groups (2021) - A. Julia - S. Nicolussi Golo - D. Vittone (preprint)

Nowhere differentiable intrinsic Lipschitz graphs (2021)

- M. Santilli (Accepted Paper:
*Comm. Partial Differential Equations*)

Distance functions with dense singular sets (2021) - A. Chambolle - M. Novaga (Accepted Paper:
*Ann. Scuola Normale Sup. Pisa*)

Anisotropic and crystalline mean curvature flow of mean-convex sets (2020) - S. Daneri - E. Radici - E. Runa (Submitted Paper)

Deterministic particle approximation of aggregation-diffusion equations on unbounded domains (2020) - S. Fagioli - E. Radici (
*Kinetic and Related Models*)

Opinion formation system via deterministic particle approximation (2020) - D. Campbell - A. Pratelli - E. Radici (Accepted Paper:
*Journal of Mathematical Analysis and Applications*)

Comparison between non-crossing and non-crossing on lines properties (2021) - N. Fusco - A. Pratelli (
*COCV*)

Sharp stability for the Riesz potential (2020) - M. Friedrich - M. Perugini - F. Solombrino (
*Journal of Functional Analysis*)

Lower semicontinuity for functionals defined on piecewise rigid functions and on $GSBD$ (2021) - L. Brasco (Accepted Paper:
*Bruno Pini Math. Anal. Semin.*)

On principal frequencies and inradius in convex sets (2018) - N. Ansini - S. Fagioli (
*Comm Math Sci.*)

Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation (2020) - L. Brasco - D. Gómez-Castro - J. L. Vazquez (Submitted Paper)

Characterisation of homogeneous fractional Sobolev spaces (2020) - F. Prinari - M. Eleuteri (
*Nonlinear Analysis: RealWorld Applications*)

$Γ$-convergence for power-law functionals with variable exponents (2020) - L. Briani - G. Buttazzo - F. Prinari (
*AMO*)

Some inequalities involving perimeter and torsional rigidity (2020) - F. Cagnetti - A. Chambolle - M. Perugini - L. Scardia (
*J. Convex Anal.*)

An extension result for generalised special functions of bounded deformation (2021) - F. Sapio (preprint)

A dynamic model for viscoelasticity in domains with time-dependent cracks (2020) - C. Mantegazza - M. Pozzetta (Accepted Paper:
*Calc. Var.*)

The Lojasiewicz-Simon Inequality for the Elastic Flow (2020) - W. Borrelli - R. Carlone - L. Tentarelli (
*Journal of Differential Equations*)

On the nonlinear Dirac equation on noncompact metric graphs (2021) - M. Degiovanni - D. Mazzoleni (Accepted Paper:
*J. London Math. Soc.*)

Optimization results for the higher eigenvalues of the $p$-Laplacian associated with sign-changing capacitary measures (2019) - A. Cesaroni - S. Dipierro - M. Novaga - E. Valdinoci (Accepted Paper:
*Annali Mat. Pura e Appl.*)

Heteroclinic connections and Dirichlet problems for a nonlocal functional of oscillation type (2018) - V. Magnani (
*Proc. Roy. Soc. Edinburgh Sect. A*)

On a measure-theoretic area formula (2015) - G. M. Leccese - V. Magnani (Submitted Paper)

A study of measure-theoretic area formulas (2020) - C. De Lellis - M. Focardi - S. Ghinassi (Preprint)

Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan (2020) - A. Braides - V. Vallocchia (Accepted Paper:
*COCV*)

Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems (2021) - M. Carioni - A. Marchese - A. Massaccesi - A. Pluda - R. Tione (
*Nonlinear Anal.*)

The oriented mailing problem and its convex relaxation (2020) - M. Carioni - A. Pluda (
*ESAIM Control Optim. Calc. Var.*)

Calibrations for minimal networks in a covering space setting (2020) - H. Garcke - J. Menzel - A. Pluda (
*Comm. Partial Differential Equations*)

Long Time Existence of Solutions to an Elastic Flow of Networks (2020)