1,468 research outputs found
A symmetry result on Reinhardt domains
We show the following symmetry property of a bounded Reinhardt domain
in : let be the smooth boundary
of and let be the Second Fundamental Form of ; if the
coefficient related to the characteristic direction is constant
then is a sphere. In Appendix we state the result from an hamiltonian point
of view
Graphs with prescribed the trace of the Levi form
We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic problems and by building Lipschitz continuous barriers
The Rabinowitz-Floer homology for a class of semilinear problems and applications
In this paper, we construct a Rabinowitz-Floer type homology for a class of
non-linear problems having a \emph{starshaped} potential; we consider some
equivariant cases as well. We give an explicit computation of the homology and
we apply it to obtain results of existence and multiplicity of solutions for
several model equations.Comment: 32 pages. arXiv admin note: substantial text overlap with
arXiv:1303.500
Integral Formulas for a Class of Curvature PDE'S and Application to Isoperimetric Inequalities and to Symmetry Problems
We prove integral formulas for closed hypersurfaces in C^(n+1); which
furnish a relation between elementary symmetric functions in the eigenvalues of
the complex Hessian matrix of the defining function and the Levi curvatures of
the hypersurface. Then we follow the Reilly approach to prove an isoperimetric
inequality. As an application, we obtain the "Soap Bubble Theorem" for star-
shaped domains with positive and constant Levi curvatures bounding the classical
mean curvature from above
On Dialetheic Entailment
The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not âfall foulâ of Curryâs Paradox by invalidating an inference rule called âAbsorptionâ (or âContractionâ) and the classical logical theorem called âAssertionâ. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priestâs counterexamples to Absorption and Assertion use in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priestâs claim that the entailment connective expresses the notion of logical consequence
Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian
In this paper we prove the existence of nonsmooth viscosity solutions for
Dirichlet problems involving elementary symmetric functions of the eigenvalues
of the complex Hessian
- âŠ