Department of Mathematics¹
Borough of Manhattan Community College
The City University of New York
New York, New York

Department of Mathematics and Statistics²
University of West Florida
Pensacola, Florida

Department of Mathematical Sciences³
William Rainey Harper College
Palatine, Illinois

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

We discover bi-harmonic maps’ existence, energy growth, and connections to harmonic maps. A nontrivial bi-harmonic map’s existence in a unit sphere is proved. We investigate the p-balanced energy as energy technical breakthroughs to break the constraints of the existing q-energy technique in detecting q-energy towards boundlessness. We study the connections between bi-harmonic maps and harmonic maps by discovering a rigid dichotomy between infinite energy and finite constant energy.

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