Semigroup properties for the second fundamental form

  • Feng-Yu Wang

    00875 UK China
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Abstract

Let MM be a compact Riemannian manifold with boundary M\partial M and L=δ+ZL= \delta+Z for a C1C^1-vector field ZZ on MM. Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by LL, are presented for lower bound conditions on the curvature of LL and the second fundamental form of M\partial M. The main result not only generalizes the corresponding known ones on manifolds without boundary, but also clarifies the role of the second fundamental form in the analysis of the Neumann semigroup. Moreover, the Lévy-Gromov isoperimetric inequality is also studied on manifolds with boundary.

Cite this article

Feng-Yu Wang, Semigroup properties for the second fundamental form. Doc. Math. 15 (2010), pp. 527–543

DOI 10.4171/DM/305