Estimates for the Classical Parametrix for the Laplacian.
We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in and to give a sufficient condition for the complete hyperbolicity of a domain in .
The free motion of a thin elastic linear membrane is described, in a simplyfied model, by a second order linear homogeneous hyperbolic system of partial differential equations whose spatial part is the Laplace Beltrami operator acting on a Riemannian 2-dimensional manifold with boundary. We adapt the estimates of the spectrum of the Laplacian obtained in the last years by several authors for compact closed Riemannian manifolds. To make so, we use the standard technique of the doubled manifold to...
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.
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...