More Weakly Biharmonic Maps from the Ball to the Sphere

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Abstract

In this note we prove the existence of two proper biharmonic maps between the Euclidean ball of dimension bigger than four and Euclidean spheres of appropriate dimensions. We will also show that, in low dimensions, both maps are unstable critical points of the bienergy.

Original languageEnglish
Article number23
JournalJournal of Geometric Analysis
Volume35
Issue number1
DOIs
Publication statusPublished - Jan 2025

Austrian Fields of Science 2012

  • 101006 Differential geometry

Keywords

  • 53C43
  • 58E20
  • Proper biharmonic map
  • Sphere
  • Stability

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