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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...

Evolution of convex entire graphs by curvature flows

Roberta Alessandroni, Carlo Sinestrari (2015)

Geometric Flows

We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature...

Example of a six-dimensional LCK solvmanifold

Hiroshi Sawai (2017)

Complex Manifolds

The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.

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