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

- Two-year postdoctoral position in analysis at EPFL Lausanne (deadline: 1 Nov 2019)
- Tenure-Track Assistant Professor of Mathematics at EPFL Lausanne (deadline: 1 Nov 2019)
- Assistant Professor or higher, Department of Applied Mathematics, University of Waterloo, Canada (deadline: 1 Dec 2019)
- Postdoctoral Researcher at Okinawa Institute of Science and Technology under Prof. Daniel Spector (deadline: 15 Dec 2019)
- 4-year PhD student in Probability and Analysis in Eindhoven (deadline: 15 Dec 2019)
- Two-year postdoctoral position in geometric analysis at University of Paris (deadline: 18 Jan 2020)

- 14 Oct 2019:
**J. H. Cheng:***Heat kernel and local index theorem for open complex manifolds with $\mathbb{C}^{\ast }$ action* - 16 Oct 2019:
**S. Don:***A rectifiability result for sets of finite perimeter in Carnot groups*

- 1 Sep - 30 Nov 2019: Simons Semester in Geometry and Analysis Warsaw & Bedlewo, Poland
- 28 - 31 Oct 2019: Calculus of Variations and Applications in Trani Trani (BT), Italy
- 29 Oct - 1 Nov 2019: Mathematics for Mechanics Czech Academy of Sciences, Prague
- 11 - 15 Nov 2019: Modeling of Crystalline Interfaces and Thin Film Structures: A Joint Mathematics-Physics Symposium Erwin Schrödinger International Institute (ESI), Vienna
- 22 - 22 Nov 2019: Incontri di Analisi Matematica tra Firenze, Pisa e Siena aula magna, dipartimento di matematica, università di Pisa
- 25 - 28 Nov 2019: Recent trends in Geometric analysis and applications Pisa: Centro De Giorgi
- 25 - 29 Nov 2019: Winter School "Gradient Flows and Variational Methods in PDEs" University Ulm
- 28 - 29 Nov 2019: Two days on CalcVar&PDEs Dipartimento di Matematica, Università di Bologna
- 13 - 15 Jan 2020: Winter School on Reaction Diffusion PDE's and Optimization Dipartimento di Matematica e Fisica, Univ. Cattolica di Brescia
- 27 - 31 Jan 2020: Winter School: Turbulence in fluids and PDEs EPFL, Lausanne, Switzerland
- 27 Jan - 1 Feb 2020: Calculus of Variations and Applications (on the occasion of Gianni Dal Maso's birthday) Trieste, SISSA
- 30 - 31 Jan 2020: Nonlinear meeting in Milan Politecnico di Milano
- 23 - 27 Mar 2020: Geometric Variational Problems University Ulm
- 8 - 12 Jun 2020: Workshop "Variational methods and applications" Centro De Giorgi, Pisa

- E. Le Donne - R. Young (preprint)

Carnot rectifiability of sub-Riemannian manifolds with constant tangent (2019) - E. Le Donne - R. Züst (preprint)

Space of signatures as inverse limits of Carnot groups (2019) - S. Piontek - T. Schmidt (Accepted Paper:
*ESAIM, Control Optim. Calc. Var.*)

Higher integrability for the gradient of Mumford-Shah almost-minimizers (2019) - M. Caponi (Ph.D. Thesis)

On some mathematical problems in fracture dynamics (2019) - I. Lucardesi - D. Zucco (Preprint)

On Blaschke-Santal\'o diagrams for the torsional rigidity and the first Dirichlet eigenvalue (2019) - A. Cesaroni - M. Novaga (Submitted Paper)

Nonlocal minimal clusters in the plane (2019) - P. Bonicatto - E. Marconi (Preprint)

Regularity estimates for the flow of BV autonomous divergence free vector fields in $\mathbb{R}^2$ (2019) - Y. Giga - F. Onoue - K. Takasao (Preprint)

A varifold formulation of mean curvature ow with Dirichlet or dynamic boundary conditions (2018) - F. Onoue (Preprint)

Nonexistence of Minimizers for a Nonlocal Perimeter Functional with a Riesz and a Background Potential (2019) - M. Vedovato (Preprint)

Quantitative regularity for $p$-minimizing maps through a Reifenberg Theorem (2019) - N. Edelen - L. Spolaor (Submitted Paper)

Regularity of minimal surfaces near quadratic cones (2019) - O. Chodosh - M. Engelstein - L. Spolaor (Submitted Paper)

The Riemannian quantitative isoperimetric inequality (2019) - H. M. Nguyen - M. Squassina (
*Journal d'Analyse Mathématique*)

On Hardy and Caffarelli-Kohn-Nirenberg inequalities (2019) - A. Braides - M. Solci (Preprint)

Compactness by coarse-graining in long-range lattice systems (2019) - M. Novaga - M. Pozzetta (Submitted Paper)

Connected surfaces with boundary minimizing the Willmore energy (2019) - C. De Lellis - G. De Philippis - B. Kirchheim - R. Tione (Submitted Paper)

Geometric measure theory and differential inclusions (2019)

- V. Georgiev - E. Stepanov (
*Discrete Contin. Dyn. Syst.*)

Metric cycles, curves and solenoids (2014) - S. Kryzhevich - E. Stepanov (
*J. Differential Equations*)

The saga of a fish: from a survival guide to closing lemmas (2019) - E. Paolini - E. Stepanov (
*J. Funct. Anal.*)

Decomposition of acyclic normal currents in a metric space (2012) - S. Kholmatov - P. Piovano (Submitted Paper)

A unified model for stress-driven rearrangement instabilities (2019) - M. Bardi - A. Goffi (
*Calc. Var. Partial Differential Equations*)

New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs (2019) - T. Schmidt (Habilitation Thesis)

$\rm BV$ Minimizers of Variational Integrals: Existence, Uniqueness, Regularity (2015) - M. Caponi - F. Sapio (Submitted Paper)

A dynamic model for viscoelastic materials with prescribed growing cracks (2019) - M. Caponi - I. Lucardesi - E. Tasso (Submitted Paper)

Energy-dissipation balance of a smooth moving crack (2018) - M. Caponi (Submitted Paper)

Existence of solutions to a phase-field model of dynamic fracture with a crack-dependent dissipation (2018) - A. Braides - A. Tribuzio (Accepted Paper:
*Discrete and Continuous Dynamical Systems Series S*)

Perturbed minimizing movements of families of functionals (2019) - G. Mercier - M. Novaga - P. Pozzi (
*Comm. Anal. Geom.*)

Anisotropic curvature flow of immersed curves (2019) - S. Bianchini - E. Marconi (
*Arch. Ration. Mech. Anal.*)

On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension (2017) - E. Marconi (
*Journal of Hyperbolic Differential Equations*)

Regularity estimates for scalar conservation laws in one space dimension (2018) - G. Catino - P. Mastrolia (
*J. Geom. Anal.*)

Weyl scalars on compact Ricci solitons (2019) - C. Mantegazza (Accepted Paper:
*Rend. Semin. Mat. Univ. Padova*)

Some Elementary Questions in the Calculus of Variations (2018) - P. Baldi - E. Haus - C. Mantegazza (Accepted Paper:
*Math. Ann.*)

Existence of a Lens–Shaped Cluster of Surfaces Self–Shrinking by Mean Curvature (2018) - D. Castorina - C. Mantegazza - B. Sciunzi (Accepted Paper:
*Milan J. Math.*)

A Liouville Theorem for Superlinear Heat Equations on Riemannian Manifolds (2018) - L. Brasco - G. Franzina (Preprint)

An overview on constrained critical points of Dirichlet integrals (2019) - C. Bucur - M. Squassina (Preprint)

Approximate convexity principles and applications to PDEs in convex domains (2019) - A. Cesaroni - S. Dipierro - M. Novaga - E. Valdinoci (
*Discrete Contin. Dyn. Syst. A*)

Minimizers of the $p$-oscillation functional (2019)