arXiv subjects

Baptiste Devyver

Publications and source records attributed to Baptiste Devyver.

21 records · Page 2Linked to original sources

arXiv2013

A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transform

Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive and the Ricci tensor is in $L^{\frac{n}{2}\pm ε}$ for an $ε>0$, then we prove a Gaussian estimate on the heat kernel of the Hodge Laplacian on 1-forms. This allows us to prove that, under the same hypotheses, the Riesz transform $dΔ^{-1/2}$ is bounded on $L^p$ for all $1

math.DG↗

arXiv2013

A perturbation result for the Riesz transform

We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_0$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$, which are isometric outside a compact set, and if the Riesz transform on $M_0$ is bounded on $L^q$, then for all $\frac{n}{n-2}, the Riesz transform on $M$ is bounded on $L^p$ provided that $M$ is p-hyperbolic OR $M$ has only one end.

math.AP↗

arXiv2011

On the finiteness of the Morse Index for Schrödinger operators

Let H=$Δ+V$ be a Schrödinger on a complete non-compact manifold. It is known since the work of Fischer-Colbrie and Schoen that the finiteness of the negative spectrum of $H$ implies the existence of a function $ϕ$ solution of $Hϕ=0$ outside a compact set. This has consequences for minimal surfaces and for the finiteness of spaces of harmonic sections in the Bochner method. Here we show that the converse statement also holds: if there exists $ϕ$ solution of $Hϕ=0$ outside a compact set, then $H$ has a finite number of negative eigenvalues.

math.DG↗