Semigroup properties for the second fundamental form
Feng-Yu Wang00875 UK China
Let be a compact Riemannian manifold with boundary and for a -vector field on . Several equivalent statements, including the gradient and Poincaré/log-Sobolev type inequalities of the Neumann semigroup generated by , are presented for lower bound conditions on the curvature of and the second fundamental form of . 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. 527–543DOI 10.4171/DM/305