论文标题
RCD空间上谐波功能的强大独特延续失败
Failure of strong unique continuation for harmonic functions on RCD Spaces
论文作者
论文摘要
$ rcd $ space上的谐波功能的独特延续是一个长期的开放问题，即使在亚历山德罗夫空间的环境中也鲜为人知。在本文中，我们在$ rcd（k，2）$ spaces上建立了较弱的独特延续定理，并在$的情况下为强烈的独特延续提供反例 rcd（k，n）$ space用于任何$ n \ geq 4 $和任何$ k \ in \ mathbb {r} $。
Unique continuation of harmonic functions on $RCD$ space is a long-standing open problem, with little known even in the setting of Alexandrov spaces. In this paper, we establish the weak unique continuation theorem for harmonic functions on $RCD(K,2)$ spaces and give a counterexample for strong unique continuation in the setting of $ RCD(K,N)$ space for any $N\geq 4$ and any $K\in \mathbb{R}$.
