Weak solutions of geometric flows associated to integro-differential harmonic maps
Armin Schikorra, Yannick Sire, Changyou Wang
TL;DR
This paper proves the existence of global weak solutions for geometric flows related to integro-differential harmonic maps into spheres and homogeneous manifolds, advancing understanding of such nonlocal geometric evolutions.
Contribution
It establishes the existence of weak solutions for a class of geometric flows involving integro-differential harmonic maps, a novel extension in the field.
Findings
Existence of global weak solutions proven
Applicable to harmonic maps into spheres and homogeneous manifolds
Advances understanding of nonlocal geometric flows
Abstract
The purpose of this note is to prove the existence of global weak solutions to the flow associated to integro-differential harmonic maps into spheres and Riemannian homogeneous manifolds.
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