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Existence and Blow-Up Behavior for Solutions of the Generalized Jang Equation
Existence and Blow-Up Behavior Solutions of the Generalized Jang Equation Differential Geometry
2012/6/9
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study o...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...
Spectral and stochastic properties of the $f$-Laplacian, solutions of PDE's at infinity, and geometric applications
Weighted Laplacians Feller property stochastic completeness essential spectrum gradient Ricci solitons
2011/8/26
Abstract: The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spec...
Non-degenerate solutions of universal Whitham hierarchy
non-degenerate solutions universal Whitham hierarchy Riemann sphere
2010/4/6
The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized...