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-spectral properties of Neumann Laplacians on some planar domains and show by calculation that the essential spectrum of the Neumann Laplacian on certain horns depends on p. The proof uses ideas due to E.B. Davies and B. Simon for the reduction to one-dimensional operators and...
By constructing examples which are explicit up to solving an ODE, we prove that singularities of first kind exist for the harmonic map and Yang-Mills heat flows. As a by-product, we also get a simplified proof of Ratto's/Ding's theorem about the existence of harmonic Hopf constructions.
Nous démontrons un Nullstellensatz qui établit une équivalence entre l'existence d'une identité algébrique d'un certain type, d'une part, et l'impossibilité de trouver une suite croissante de variétés irréductibles répondant à certaines contraintes d'autre part. De ce point de vue le...
In this paper we prove a characterization of the maximal viscosity subsolution for a class of Hamilton–Jacobi equations coupled with Dirichlet boundary condition for which uniqueness of the viscosity solution does not necessarily hold.
In this work we introduce a class of 2-dimensional hyperbolic buildings with prescribed local structure. We prove existence and unicity of such buildings. We show that their automorphism group is transitive on chambers. These result allow us to identify many hyperbolic buildings obtained in...
We solve the Dirichlet problem for strictly convex, spacelike hypersurfaces of prescribed Weingarten curvature under the main assumption that there exists an upper barrier. We consider curvature functions that correspond in general to fully nonlinear elliptic partial differential equations which...
We show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct a natural collection of birational transformations. These were first constructed as flips in the case of curves by M. Thaddeus via Geometric Invariant Theory, and the...
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