Poincare constant on manifolds with ends
Grigoryan, Alexander
Grigoryan
Alexander
Ishiwata, Satoshi
Ishiwata
Satoshi
Saloff-Coste, Laurent
Saloff-Coste
Laurent
We obtain optimal estimates of the Poincare constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincare constant is determined by the second largest end. The proof is based on the argument by Kusuoka-Stroock where the heat kernel estimates on the central balls play an essential role. For this purpose, we extend earlier heat kernel estimates obtained by the authors to a larger class of parabolic manifolds with ends.
Wiley
2023