Energy identity for approximations of harmonic maps from surfaces
Tobias Lamm
TL;DR
This paper establishes the energy identity for certain approximations of harmonic maps from surfaces, using estimates related to Hopf differentials and bubble concentration.
Contribution
It proves the energy identity for min-max sequences of Sacks-Uhlenbeck and biharmonic approximations, advancing understanding of harmonic map approximations.
Findings
Energy identity proven for Sacks-Uhlenbeck approximation
Energy identity proven for biharmonic approximation
Uses Hopf-differential estimates and bubble concentration analysis
Abstract
We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two approximations and on estimates for the concentration radius of bubbles.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Numerical methods in inverse problems · Geometric Analysis and Curvature Flows