Deuschel, Jean-Dominique On estimating the hypercontractive constant of a diffusion process on a compact manifold. (English) Zbl 0743.60075 Diffusion processes and related problems in analysis, Vol. I: Diffusions in analysis and geometry, Proc. Int. Conf., Evanston/IL (USA) 1989, Prog. Probab. 22, 149-154 (1990). [For the entire collection see Zbl 0716.00011.]Let \(M\) be an \(N\)-dimensional, connected, compact \(C^ \infty\) Riemannian manifold. \(\{P_ t, t>0\}\) denotes the Markov semigroup, connected with the solution of the martingale problem for \(\Delta\) on \(C^ \infty(M)\) at \(x,x\in M\), where \(\Delta\) is the Laplacian. Some estimates of the hypercontractive constant of \(\{P_ t, t>0\}\) are given in terms of the geometry of \(M\). Reviewer: Wu Rong (Tianjin) Cited in 1 Document MSC: 60J60 Diffusion processes 47D07 Markov semigroups and applications to diffusion processes Keywords:diffusion process; compact manifold; Markov semigroup; martingale problem; hypercontractive Citations:Zbl 0716.00011 PDFBibTeX XMLCite \textit{J.-D. Deuschel}, Prog. Probab. None, 149--154 (1990; Zbl 0743.60075)