Unique continuation problem on RCD spaces

Abstract: In this talk we will sketch the proof of the unique continuation property of harmonic functions and caloric functions on any RCD(K,2) spaces and a counterexample for the strong unique continuation property of harmonic function on an RCD(K,4) space. This characterizes one of the significant differences between RCD spaces and smooth manifolds. We will also talk about some related open problems. The talk is based on joint works with Qin Deng.

Mathematics

Audience: researchers in the topic

IUT Mathematics Research Seminars (IMRS)

Series comments: All researchers are welcomed!