论文标题
椭圆形和抛物线边界价值问题旋转对称域的功率凹形
Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
论文作者
论文摘要
我们研究了旋转对称解的功率凹陷，这些解针对旋转和抛物线边界价值问题在旋转歧管中的旋转对称结构域上。作为我们在双曲空间的应用程序$ {\ bf h}^n $我们有： $ \ bullet $在$ {\ bf h}^n $中的球上的第一个dirichlet eigenfunction是严格的正力凹点； $ \ bullet $让$γ$是$ {\ bf H}^n $上的热核。然后，$γ（\ cdot，y，t）$是$ {\ bf h}^n $在{\ bf h}^n $ in {\ bf h}^n $和$ t> 0 $的$ {\ bf h}^n $上的log-concave。
We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applications of our results to the hyperbolic space ${\bf H}^N$ we have: $\bullet$ The first Dirichlet eigenfunction on a ball in ${\bf H}^N$ is strictly positive power concave; $\bullet$ Let $Γ$ be the heat kernel on ${\bf H}^N$. Then $Γ(\cdot,y,t)$ is strictly log-concave on ${\bf H}^N$ for $y\in {\bf H}^N$ and $t>0$.
