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Some analytic results on interpolating sesqui-harmonic maps.

Volker Branding1

  • 1Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.

Annali Di Matematica Pura Ed Applicata
|September 21, 2020
PubMed
Summary

This study examines interpolating sesqui-harmonic maps on Riemannian manifolds, focusing on spherical targets. We establish a conservation law to prove solution smoothness and achieve classification results.

Keywords:
Classification resultsInterpolating sesqui-harmonic mapsRegularity of weak solutions

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Area of Science:

  • Differential Geometry
  • Geometric Analysis
  • Topology

Background:

  • Harmonic and biharmonic maps are fundamental in geometric analysis.
  • Interpolating sesqui-harmonic maps bridge these concepts via a novel energy functional.
  • Understanding their analytic properties is crucial for advancing geometric mapping theories.

Purpose of the Study:

  • To investigate the analytic properties of interpolating sesqui-harmonic maps.
  • To focus on the specific case where the target manifold is a sphere.
  • To derive key results regarding the behavior and classification of these maps.

Main Methods:

  • Analysis of critical points of an energy functional.
  • Derivation of a conservation law for maps with spherical targets.
  • Techniques to demonstrate the smoothness of weak solutions.
  • Classification of interpolating sesqui-harmonic maps.

Main Results:

  • A conservation law is derived for interpolating sesqui-harmonic maps onto a sphere.
  • The smoothness of weak solutions is established using the conservation law.
  • Several classification results for these maps are obtained.

Conclusions:

  • The study provides significant analytic insights into interpolating sesqui-harmonic maps.
  • The findings contribute to the understanding of geometric mappings and their properties.
  • The derived conservation law and classification results offer a foundation for future research.