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)
- Vectorial Elliptic, Parabolic and Variational Problems: Singularities and Regularity (Giuseppe Mingione)
- Analysis of Optimal Sets and Optimal Constants: Old Questions and New Results (Aldo Pratelli)
- Mathematics for Shape Memory Technologies in Biomechanics (Ulisse Stefanelli)

- Lecturer in Mathematics at the University of Sussex (deadline: 27 Jul 2017)
- Postdoc Position in Freiburg (Germany) (deadline: 30 Jul 2017)
- PhD Position in Freiburg (Germany) (deadline: 30 Jul 2017)
- 9 PhD positions in Mathematics at Sapienza University (deadline: 31 Jul 2017)
- Lecturer/Senior Lecturer or Reader in Mathematics at the University of Sussex (deadline: 10 Aug 2017)

- 14 - 19 Aug 2017: Mathematics in the Modern World Novosibirsk, Russia
- 6 - 8 Sep 2017: IperPV2017 Pavia
- 14 - 15 Sep 2017: Workshop "Calculus of Variations and Partial Differential Equations" Università degli Studi di Napoli Federico II
- 18 - 20 Sep 2017: 4th Conference on Recent Trends in Nonlinear Phenomena Messina
- 21 - 22 Sep 2017: Nonlinear Days in Turin Turin
- 2 - 6 Oct 2017: Harmonic Analysis and Geometric measure Theory CIRM (Marseille, France)
- 9 - 13 Oct 2017: Geometric Analysis at Roscoff Roscoff, France

- R. Monti - A. Pigati - D. Vittone (Preprint)

On tangent cones to length minimizers in Carnot-Carathéodory spaces (2017) - D. Bartolucci - D. Castorina (Accepted Paper:
*Annali della Scuola Normale Superiore di Pisa-Classe di Scienze*)

On a singular Liouville-type equation and the Alexandrov isoperimetric inequality (2017) - P. Antonini - G. De Philippis - N. Gigli (Submitted Paper)

The injectivity radius of Lie manifolds (2017) - F. Ferrari - M. J. Miranda - D. Pallara - A. Pinamonti - Y. Sire (Submitted Paper)

Fractional Laplacians, perimeters and heat semigroups in Carnot groups (2017) - E. Mainini - M. Monteverde - E. Oudet - D. Percivale (Preprint)

The minimal resistance problem in a class of non convex bodies (2017) - A. Marchese (Preprint)

Residually many BV homeomorphisms map a null set in a set of full measure (2017) - A. Cesaroni - M. Novaga (Submitted Paper)

The isoperimetric problem for nonlocal perimeters (2017) - A. Ponce - D. Spector (Preprint)

A note on the Fractional Perimeter and Interpolation (2017) - A. Pratelli - E. Radici (Preprint)

Approximation of planar BV homeomorphisms by diffeomorphisms (2017) - A. Pratelli - E. Radici (Preprint)

On the planar minimal BV extension problem (2017) - F. Dragoni - E. Feleqi (Submitted Paper)

PDEs from ergodic Mean Field Games with Hoermander diffusions (2017) - N. Dirr - F. Dragoni - M. von Renesse (preprint)

Evolution by mean curvature in sub-Riemannian geometries: A stochastic approach (2008) - N. Dirr - F. Dragoni - P. Mannucci - C. Marchi (Submitted Paper)

Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations (2017) - N. Fusco - V. Julin - M. Morini (Submitted Paper)

The surface diffusion flow with elasticity in the plane (2017) - G. Cupini - N. Fusco - E. Lanconelli (Submitted Paper)

A sharp stability result for the Gauss mean value formula (2017) - F. Cavalletti - F. Maggi - A. Mondino (Preprint)

Quantitative isoperimetry à la Levy-Gromov (2017) - V. Crismale - G. Orlando (preprint)

A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in $W^{1,n}$ (2017)

- T. K. Nguyen - D. Vittone (
*J. Convex Anal.*)

Rectifiability of special singularities of non-Lipschitz functions (2012) - D. Vittone (
*Ann. Scuola Norm. Sup. Pisa Cl. Sci.*)

Lipschitz surfaces, perimeter and trace theorems for BV functions in Carnot-Carathèodory spaces (2012) - E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone (
*GAFA Geometric and Functional Analysis*)

Extremal curves in nilpotent Lie groups (2013) - A. Marigonda - T. K. Nguyen - D. Vittone (
*Indiana Univ. Math. J.*)

Some regularity results for a class of upper semicontinuous functions (2013) - A. Marigonda - K. T. Nguyen - D. Vittone (
*Large-scale scientific computing, Lecture Notes in Comput. Sci., 8353, Springer, Heidelberg.*)

BV regularity and differentiability properties of a class of upper semicontinuous functions (2014) - E. Le Donne - R. Montgomery - A. Ottazzi - P. Pansu - D. Vittone (
*Ann. Inst. H. Poincaré Anal. Non Linéaire*)

Sard Property for the endpoint map on some Carnot groups (2016) - A. Pinamonti - F. Serra Cassano - G. Treu - D. Vittone (
*Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)*)

BV Minimizers of the area functional in the Heisenberg group under the bounded slope condition (2015) - F. Serra Cassano - D. Vittone (
*Adv. Calc. Var.*)

Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups (2014) - D. Vittone (
*Geometric measure theory and real analysis, CRM Series, Ed. Norm., Pisa.*)

The regularity problem for sub-Riemannian geodesics (2014) - E. Le Donne - G. P. Leonardi - R. Monti - D. Vittone (
*ESAIM Control Optim. Calc. Var.*)

Corners in non-equiregular sub-Riemannian manifolds (2015) - A. Massaccesi - D. Vittone (Accepted Paper:
*J. Eur. Math. Soc. (JEMS)*)

An elementary proof of the rank-one theorem for BV functions (2016) - M. Fogagnolo - R. Monti - D. Vittone (
*Ann. Ac. Sci. Fennicae*)

Variation formulas for H-rectifiable sets (2017) - D. Vittone (Ph.D. Thesis:
*Theses of Scuola Normale Superiore di Pisa (New Series). Edizioni della Normale, Pisa.*)

Submanifolds in Carnot groups (2008) - M. Cicalese - N. Fusco (Submitted Paper)

A note on relaxation with constraints on the determinant (2017) - A. Pinamonti - G. Speight (Illinois Journal of Math. )

Structure of Porous Sets in Carnot Groups (2016) - R. Alicandro - G. Dal Maso - G. Lazzaroni - M. Palombaro (Preprint)

Linearisation of multiwell energies (2017) - G. Dal Maso - M. Morandotti (
*Nonlinear Anal.*)

A model for the quasistatic growth of cracks with fractional dimension (2017) - T. Hudson - M. Morandotti (Accepted Paper:
*SIAM J. Appl. Math*)

Properties of screw dislocation dynamics: time estimates on boundary and interior collisions (2017) - A. C. Barroso - J. Matias - M. Morandotti - D. R. Owen (
*Math. Mech. Complex Syst.*)

Explicit Formulas for Relaxed Disarrangement Densities Arising from Structured Deformations (2017) - G. A. Bonaschi - P. van Meurs - M. Morandotti (
*Eur. J. Appl. Math.*)

Dynamics of screw dislocations: a generalised minimising-movements scheme approach (2017) - A. C. Barroso - J. Matias - M. Morandotti - D. R. Owen (
*Arch. Rational Mech. Anal.*)

Second-order structured deformations: relaxation, integral representation and applications (2017) - M. Bongini - M. Fornasier - F. Rossi - F. Solombrino (Accepted Paper:
*Journal of Optimization Theory and Applications*)

Mean-field Pontryagin Maximum Principle (2015) - A. Pratelli - E. Radici (Accepted)

On the piecewise approximation of bi-Lipschitz curves (2015) - A. Chambolle - J. Lamboley - A. Lemenant - E. Stepanov (
*SIAM J. Math. Anal.*)

Regularity for the optimal compliance problem with length penalization (2017) - E. Stepanov - Y. Teplitskaya (Accepted Paper:
*J. London Math. Soc.*)

Self-contracted curves have finite length (2016) - A. Braides - A. Malusa - M. Novaga (Submitted Paper)

Crystalline evolutions with rapidly oscillating forcing terms (2017)