| Título: | Some Remarks on the Heat Flow for Functions and Forms |
| Autores: | Thalmaier, Anton; University of Bonn |
| Fecha: | 1998-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Heat semigroup, heat equation, Brownian motion, damped parallel translation, Ricci curvature. 58G32, 60H10, 60H30. |
| Descripción: | This note is concerned with the differentiation of heat semigroups on Riemannian manifolds. In particular, the relation $dP_tf=P_tdf$ is investigated for the semigroup generated by the Laplacian with Dirichlet boundary conditions. By means of elementary martingale arguments it is shown that well-known properties which hold on complete Riemannian manifolds fail if the manifold is only BM-complete. In general, even if $M$ is flat and $f$ smooth of compact support, $\Vert dP_tf\Vert_\infty$ cannot be estimated on compact time intervals in terms of $f$ or $df$. |
| Idioma: | Inglés |
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