Silvano Delladio (1996)
Annales Polonici Mathematici
We prove generalizations of Meusnier's theorem and Fenchel's inequality for a class of generalized surfaces with curvature measures. Moreover, we apply them to obtain a diameter estimate.
Andrei A. Agrachev, Francesca C. Chittaro (2009)
ESAIM: Control, Optimisation and Calculus of Variations
We study Hamiltonian systems which generate extremal flows of regular variational problems on smooth manifolds and demonstrate that negativity of the generalized curvature of such a system implies the existence of a global smooth optimal synthesis for the infinite horizon problem. We also show that in the Euclidean case negativity of the generalized curvature is a consequence of the convexity of the Lagrangian with respect to the pair of arguments. Finally, we give a generic classification for...
David G. Schaeffer (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Enrique Fernández-Cara, Thierry Horsin, Henry Kasumba (2013)
Annales mathématiques Blaise Pascal
This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.
Luis Caffarelli (2003)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Liouville problems in periodic media (i.e. the study of properties of global solutions to PDE) arise both in homogenization and dynamical systems. We discuss some recent results for minimal surfaces and free boundaries.
Giuseppe Buttazzo, Bozhidar Velichkov (2014)
Banach Center Publications
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
L. Ambrosio, M. Novaga, E. Paolini (2002)
ESAIM: Control, Optimisation and Calculus of Variations
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space ( a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is empty...
L. Ambrosio, M. Novaga, E. Paolini (2010)
ESAIM: Control, Optimisation and Calculus of Variations
We introduce an intrinsic notion of perimeter for subsets of a general Minkowski space (i.e. a finite dimensional Banach space in which the norm is not required to be even). We prove that this notion of perimeter is equivalent to the usual definition of surface energy for crystals and we study the regularity properties of the minimizers and the quasi-minimizers of perimeter. In the two-dimensional case we obtain optimal regularity results: apart from a singular set (which is -negligible and is...
Francescopaolo Montefalcone (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called-convexity, we state a Cauchy type formula for -convex sets. Finally,...
Mariano Giaquinta, Giuseppe Modica, Jiří Souček (1994)
Commentationes Mathematicae Universitatis Carolinae
We discuss variational problems for the -Dirichlet integral, non integer, for maps between manifolds, illustrating the role played by the geometry of the target manifold in their weak formulation.
F. Barthe, B. Maurey (2000)
Annales de l'I.H.P. Probabilités et statistiques
Martin Fuchs (1986)
Manuscripta mathematica
V. Caselles, M. Novaga, A. Chambolle (2010)
Rendiconti del Seminario Matematico della Università di Padova
Michael Beeson (1980)
Mathematische Zeitschrift
Michael Beeson (1982)
Mathematische Zeitschrift
Roger Züst (2015)
Analysis and Geometry in Metric Spaces
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...
L. Mangiarotti, M. Modugno (1983)
Annales de l'I.H.P. Physique théorique
Pierre Pansu (1993/1994)
Séminaire Bourbaki
Silvano Delladio (1997)
Journal für die reine und angewandte Mathematik
Karlheinz Schüffler (1979/1980)
Manuscripta mathematica