Bi-Harmonic Maps' Existence and p-Balanced Energy and Connections to Harmonic Maps

Authors

• Lina Wu, The City University of New York at Borough of Manhattan Community CollegeFollow

Document Type

Article

Publication Date

Summer 6-6-2024

Abstract

We discover a bi-harmonic map’ existence, its energy growth, and its connections to a harmonic map. First, we prove the existence of a nontrivial bi-harmonic map in a unit sphere. Second, we investigate the p-balanced energy growth of biharmonic maps. As the most important energy technical breakthroughs, we propose an innovative energy algorithm called p-balanced energy technique to break the constraints of the existing L^q-energy technique in detecting L^q-energy growth towards boundlessness. The disadvantage of the finite L^q -energy technique in the L ^q spaces is not effective in dealing with infinite L^q- energy in Non-L^q spaces. Third, we study the connections between bi-harmonic maps and harmonic maps by employing our p-balanced energy technique to discover a rigid dichotomy between infinite energy and finite constant energy. We demonstrate the theoretical verification for our research findings. The research implication of these innovative energy techniques on A-harmonic theory in physics is also discussed.

Comments

This project has been financially supported by the 2023-2024 Faculty Development Grant in The City University of New York at Borough of Manhattan Community College.