论文标题
庞加莱在多种流形上不变
Poincaré constant on manifolds with ends
论文作者
论文摘要
我们获得了有限多端的歧管上中央球的庞加莱常数的最佳估计。令人惊讶的是，庞加莱常数取决于第二大端。证明是基于Kusuoka-Strock的论点，即中央球的热核估计起着至关重要的作用。为此，我们将作者获得的早期热核估计值扩展到具有末端的较大类抛物线歧管。
We obtain optimal estimates of the Poincaré constant of central balls on manifolds with finitely many ends. Surprisingly enough, the Poincaré 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.
