Carleman Estimate for Surface in Euclidean Space at Infinity
Ao Sun
TL;DR
This paper establishes a Carleman estimate for surfaces in Euclidean space at infinity, enabling unique continuation for harmonic functions and resulting in new geometric rigidity theorems.
Contribution
It introduces a novel Carleman estimate for immersed surfaces at infinity, advancing the understanding of harmonic functions and geometric rigidity.
Findings
Unique continuation property for harmonic functions on surfaces
Rigidity results in geometric analysis
Development of a Carleman estimate at infinity
Abstract
This paper develops a Carleman type estimate for immersed surface in Euclidean space at infinity. With this estimate, we obtain an unique continuation property for harmonic functions on immersed surfaces vanishing at infinity, which leads to rigidity results in geometry.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Numerical methods in inverse problems · Geometric Analysis and Curvature Flows