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Some Remarks on the Heat Flow for Functions and Forms

   
@article{ECP992,
	author = {Anton Thalmaier},
	title = {Some Remarks on the Heat Flow for Functions and Forms},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {3},
	year = {1998},
	keywords = {Heat semigroup, heat equation, Brownian motion,  damped parallel translation, Ricci curvature.},
	abstract = {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 $df$.},
	pages = {no. 6, 43-49},
	issn = {1083-589X},
	doi = {10.1214/ECP.v3-992},    
        url = {http://ecp.ejpecp.org/article/view/992}}