Rotationally symmetric harmonic diffeomorphisms between surfaces
Li Chen, Shi-Zhong Du, Xu-Qian Fan
TL;DR
This paper proves that no rotationally symmetric harmonic diffeomorphism exists between the unit disk (excluding the origin) and a punctured disk with a hyperbolic metric.
Contribution
It establishes a nonexistence result for a specific class of harmonic diffeomorphisms between certain symmetric surfaces.
Findings
No rotationally symmetric harmonic diffeomorphism from the unit disk minus the origin to a hyperbolic punctured disk exists.
The result clarifies limitations of harmonic mappings between symmetric surfaces.
Provides insights into geometric function theory and harmonic map constraints.
Abstract
In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds