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Calculus on Normed Vector Spaces
International audience -
Counting arcs in negative curvature
42 pages -
Convexity of the Set of k-Admissible Functions on a Compact Kähler Manifold.
We prove in this article using some convex analysis results of A. S. Lewis the log-concavity of spectral elementary symmetric functions on the space of Hermitian... -
Convexity of Some Spectral Functions on Hermitian Matrices.
We prove in this note the convexity of the functions $u\circ \lambda $ and more generally $u\circ \lambda_B $ on the space of Hermitian matrices, for $B$ a fixed... -
Representation, relaxation and convexity for variational problems in Wiener s...
We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation... -
On the number of simple arrangements of five double pseudolines
International audience -
Optimal Transport : Regularity and applications
This thesis consists in two distinct parts both related to the optimal transport theory.The first part deals with the regularity of the optimal transport map. The key... -
ANALYTICAL PARAMETERIZATION OF ROTORS AND PROOF OF A GOLDBERG CONJECTURE BY O...
International audience -
Computing rational solutions of linear matrix inequalities
International audience -
Thin r-neighborhoods of embedded geodesics with finite length and negative Ja...
preprint, final version 25 pages -
Two properties of volume growth entropy in Hilbert geometry
The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may... -
Convexities and optimal transport problems on the Wiener space
The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe... -
Pursuit-evasion, decompositions and convexity on graphs
This thesis focuses on the study of structural properties of graphs whose understanding enables the design of efficient algorithms for solving optimization problems.... -
Metric Spaces, Convexity and Nonpositive Curvature (Second edition)
International audience -
On the convexity of injectivity domains on nonfocal manifolds
International audience -
A tau-conjecture for Newton polygons
One can associate to any bivariate polynomial P(X,Y) its Newton polygon. This is the convex hull of the points (i,j) such that the monomial X^i Y^j appears in P with a... -
A nonstandard free boundary problem arising in the shape optimization of thin...
International audience
