Affiliation:
1. Department of Mathematics, University of Chicago, 5734 S University Ave , Chicago IL , 60637 , United States
Abstract
Abstract
In this article, we prove a Carleman inequality on a product manifold
M
×
R
M\times {\mathbb{R}}
. As applications, we prove that (1) a periodic harmonic function on
R
2
{{\mathbb{R}}}^{2}
that decays faster than all exponential rate in one direction must be constant 0, (2) a periodic minimal hypersurface in
R
3
{{\mathbb{R}}}^{3}
that has an end asymptotic to a hyperplane faster than all exponential rate in one direction must be a hyperplane, and (3) a periodic translator in
R
3
{{\mathbb{R}}}^{3}
that has an end asymptotic to a hyperplane faster than all exponential rates in one direction must be a translating hyperplane.
Subject
General Mathematics,Statistical and Nonlinear Physics
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