常曲率空间中的Matzoh球汤
Matzoh ball soup in spaces of constant curvature
摘要：
本文将Magnanini-Sakaguchi [MS 3]的结果从欧几里得空间推广到常曲率空间.更精确地说，我们证明了，如果在常曲率常曲率空间中，满足外部测地球条件的导体具有初始温度0，并且其边界保持在温度1（在任何时候），如果导体的热导率是其度量的倒数，并且如果导体包含适当的子域，满足内测地线锥条件且在给定时刻边界温度恒定，则导体一定是测地线球。此外，我们还证明了常曲率空间中波动方程和薛定谔方程的类似结果。
英文摘要：
In this paper, we generalize Magnanini-Sakaguchi's result [MS3] from Euclidean space to spaces of constant curvature. More precisely, we show that if a conductor satisfying the exterior geodesic sphere condition in the space of constant curvature has initial temperature 0 and its boundary is kept at temperature 1 (at all times), if the thermal conductivity of the conductor is inverse of its metric, and if the conductor contains a proper sub-domain, satisfying the interior geodesic cone condition and having constant boundary temperature at each given time, then the conductor must be a geodesic ball. Moreover, we show similar result for the wave equations and the Schrödinger equations in spaces of constant curvature.
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