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Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space

Ge Yuxin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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 des différences de corps convexes plans

Yves Martinez-Maure (1999)

Annales Polonici Mathematici

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...

Exemples d'applications holomorphes d'indice un

Rabah Souam (1993)

Annales de l'institut Fourier

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 of H-bubbles in a perturbative setting.

Paolo Caldiroli, Roberta Musina (2004)

Revista Matemática Iberoamericana

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..

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