标题： 黎曼流形上热源猜想的共形坐标 显示英文标题

标题： The hot spots conjecture on Riemannian manifolds with isothermal coordinates

摘要： 在本文中，我们研究具有共形坐标和解析度量的黎曼流形上的热点猜想，例如双曲空间$\mathbb{D}^n$和球面$S^n$对于$n\geq 2$。我们证明了对于此类黎曼流形中的一些（可能不是凸的）Lipschitz 域，这些域是 $\mathbb{R}^2$中的 lip 域和具有两个对称轴的对称域的推广，热点猜想成立。 显示英文摘要

摘要： In this paper, we study the hot spots conjecture on Riemannian manifolds with isothermal coordinates and analytic metrics, such as hyperbolic spaces $\mathbb{D}^n$ and spheres $S^n$ for $n\geq 2$. We prove that for some (possibly non-convex) Lipschitz domains in such a Riemannian manifold, which are generalizations of lip domains and symmetric domains with two axes of symmetry in $\mathbb{R}^2$, the hot spot conjecture holds.