Energy reduction for Fourth order Willmore energy

Q: What type of study is this?

This is a Quantitative Study study.

Nan Wu; Zetian Yan

doi:10.48550/arxiv.2504.08105

April 10, 2025Open Access

Energy reduction for Fourth order Willmore energy

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Key Points

This research establishes a significant reduction in energy for closed four-dimensional submanifolds, advancing the understanding of Willmore-type problems.
The connected sum energy reduction mirrors the foundational results found in prior works by Bauer and Kuwert, reinforcing its importance.
A focus on fourth-order Willmore energy provides new insights into the geometric properties of immersed manifolds in higher-dimensional spaces.
This approach offers potential applications in geometric analysis and the study of variational problems in differential geometry.

Implication

We establish a connected sum energy reduction for closed four-dimensional submanifolds, highlighting similarities with past work by Bauer and Kuwert.

Abstract

We introduce a fourth-order Willmore-type problem for closed four-dimensional submanifolds immersed in Rⁿ and establish a connected sum energy reduction for the general fourth-order Willmore energy, analogous to the seminal result of Bauer and Kuwert {Bauer-Kuwert03}.

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Cite This Study

Wu et al. (2025) studied this question.

synapsesocial.com/papers/68da58d1c1728099cfd10e8f https://doi.org/10.48550/arxiv.2504.08105

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Energy reduction for Fourth order Willmore energy

Key Points

Implication

Abstract

Discussion

Cite This Study

Energy reduction for Fourth order Willmore energy

Key Points

Implication

Abstract

Discussion

Cite This Study

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