A nonexistence result on harmonic diffeomorphisms between punctured spaces
Shi-Zhong Du, Xu-Qian Fan
TL;DR
This paper proves a nonexistence result for harmonic diffeomorphisms between punctured Euclidean and hyperbolic spaces, providing an elementary proof for the case of rotational symmetry.
Contribution
It establishes a new nonexistence theorem for harmonic diffeomorphisms between punctured spaces with an elementary proof for rotationally symmetric cases.
Findings
Harmonic diffeomorphisms do not exist between punctured Euclidean and hyperbolic spaces.
Elementary proof provided for rotationally symmetric cases.
Clarifies limitations of harmonic mappings between these spaces.
Abstract
In this paper, we will prove a result of nonexistence on harmonic diffeomorphisms between punctured spaces. In particular, we will given an elementary proof to the nonexistence of rotationally symmetric harmonic diffeomorphisms from the punctured Euclidean space onto the punctured hyperbolic space.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research