Michiaki Onodera, Tokyo Institute of Technology
601, Pao Yue-Kong Library
I will present a rigidity result on an overdetermined problem, in which one needs to determine the shape of a planet inducing a prescribed gravitational field. The main idea is to introduce a flow which appears as a deformation process for a parametrized “stationary” problem. Spectral analysis for the linearized flow yields a detailed stability estimate for solutions to the overdetermined problem.