Gradient estimates for the heat semigroup on forms in a complete Riemannian manifold
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:55:25Z | |
| dc.date.available | 2024-04-04T02:55:25Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192362 | |
| dc.description.abstractEn | We study the heat equation $\frac{\partial u}{\partial t}-\Delta u=0,\ u(x,0)=\omega (x),$ where $\Delta :=dd^{*}+d^{*}d$ is the Hodge laplacian and $u(\cdot ,t)$ and $\omega $ are $p$-differential forms in the complete Riemannian manifold $(M,g).$ Under weak bounded geometrical assumptions we get estimates on its semigroup of the form: acting on $p$-forms with $p\geq 1$ and $k\geq 0$: $\displaystyle \forall t\geq 1,\ {\left\Vert{\nabla ^{k}e^{-t\Delta_{p}}}\right\Vert}_{L^{r}(M)-L^{r}(M)}\leq c(n,r,k).$ Acting on functions, i.e. with $p=0,$ we get a better result: $\displaystyle \forall k\geq 1,\ \forall t\geq 1,\ {\left\Vert{\nabla ^{k}e^{-t\Delta }}\right\Vert}_{L^{r}(M)-L^{r}(M)}\leq c(n,r,k)t^{-1/2}.$ | |
| dc.language.iso | en | |
| dc.title.en | Gradient estimates for the heat semigroup on forms in a complete Riemannian manifold | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 2003.03985 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02506593 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02506593v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AMAR,%20Eric&rft.genre=preprint |
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