Energy reduction for Fourth order Willmore energy
Differential Geometry
2025-05-27 v3
Abstract
We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in and establish a connected sum energy reduction for the general fourth-order Willmore energy, analogous to the seminal result of Bauer and Kuwert \cite{Bauer-Kuwert03}.
Cite
@article{arxiv.2504.08105,
title = {Energy reduction for Fourth order Willmore energy},
author = {Nan Wu and Zetian Yan},
journal= {arXiv preprint arXiv:2504.08105},
year = {2025}
}
Comments
47 pages. Comments are welcome. There is a mistake in Lemma 5.7 of the previous version, which implies that the energy reduction result holds only for manifolds that are both non-umbilic. Consequently, we can establish an energy reduction criterion that may help prevent topology loss, rather than a non-existence result