Estimates for Evolutionary Surfaces of Prescribed Mean Curvature.
Estimates of the first eigenvalue of a big cup domain of a 2-sphere
Estimation of the best constant involving the norm of the higher-order Wente problem.
Estimation of the visibility angle of a curve in a metric space of nonpositive curvature.
Estimations of the best constant involving the norm in Wente’s inequality and compact -surfaces in euclidean space
Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space
In the first part of this paper, we study the best constant involving the L2 norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes.
Étude analytique sur la cyclide
Étude des différences de corps convexes plans
We characterize the linear space ℋ of differences of support functions of convex bodies of 𝔼² and we consider every h ∈ ℋ as the support function of a generalized hedgehog (a rectifiable closed curve having exactly one oriented support line in each direction). The mixed area (for plane convex bodies identified with their support functions) has a symmetric bilinear extension to ℋ which can be interpreted as a mixed area for generalized hedgehogs. We study generalized hedgehogs and we extend the...
Euclidean Hypersurfaces with Isometric Gauss Maps.
Euclidean Submanifolds with Nonparallel Normal Space.
Euler-Savary's formula on Minkowski geometry.
Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
We relate the total curvature and the isoperimetric deficit of a curve in a two-dimensional space of constant curvature with the area enclosed by the evolute of . We provide also a Gauss-Bonnet theorem for a special class of evolutes.
Exceptional smooth Bol loops.
Exemples d'applications holomorphes d'indice un
Nous construisons une famille de surfaces de Riemann hyperelliptiques, de genre variable, munies de fonctions méromorphes de degré deux et d’indice un, ce qui apporte une réponse positive à une conjecture de S. Montiel et A. Ros.
Existence and Non Existence of Capillary Surfaces.
Existence and regularity of hypersurfaces with prescribed mean curvature and a free boundary.
Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface.
Existence de surfaces de Willmore qui ne sont pas minimales
Existence of embedded solutions of Plateau's problem
Existence of H-bubbles in a perturbative setting.
Given a C1 function H: R3 --> R, we look for H-bubbles, i.e., surfaces in R3 parametrized by the sphere S2 with mean curvature H at every regular point..