Affiliation:
1. Department of Mathematics , Massachusetts Institute of Technology , 77 Massachusetts Ave, MA 02139 , Cambridge , USA
Abstract
Abstract
Unique continuation of harmonic functions on
RCD
{\operatorname{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
)
{\operatorname{RCD}(K,2)}
spaces and give a counterexample for strong unique continuation in the setting of
RCD
(
K
,
N
)
{\operatorname{RCD}(K,N)}
space for any
N
≥
4
{N\geq 4}
and any
K
∈
ℝ
{K\in\mathbb{R}}
.
Subject
Applied Mathematics,General Mathematics
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