Estimates on the modulus of expansion for vector fields solving nonlinear equations

Details Estimates on the modulus of expansion for vector fields solving nonlinear equations Estimates on the modulus of expansion for vector fields solving nonlinear equations

2011-07-12

arxiv.org/abs/1107.2351v1

Mathematics

Differential Geometry

Scientific paper

By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, which improves an earlier work of Brascamp-Lieb. We also include alternate proofs to the improved log-concavity estimate, and to the fundamental gap theorem of Andrews-Clutterbuck via the elliptic maximum principle. Some applications of the estimates are also obtained, including a sharp lower bound on the first eigenvalue.

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