PreprintCC0arXiv
The rigidity theorems for complete self-expander of mean curvature flow
Abstract
Our first main result is a rigidity theorem for complete self-expanders in the Euclidean space with higher codimension, assuming an integral cur More precisely, any smooth complete self-expander x:M→ ℝn+p(n≥3) that satisfies both (∫M|A|ndμ)1/n<K(n) and ∫M|A|ne|x|2/2dμ<∞ for a positive constant K(n) depending only o isometric to ℝn. Moreover, we show that the rigidity result persists when the pinching condition is expressed in terms of the trace-free second fundamental form.
Related
- Rigidity theorems of complete self-shrinkers in the Euclidean space
- Eigenvalue comparison theorems for the Witten-Laplacian and the weighted p-Laplacian on complete manifolds with a modified Ricci curvature bounded from below
- Rigidity of Ricci-Pinched Complete Self-Shrinkers in Arbitrary Codimension
- Instability of mean curvature flow in expander coordinates
- Complete Self-Shrinkers in Arbitrary Codimension with Positive Constant Scalar Curvature and S≤ 1
BibTeX
@misc{li2026rigidity,
title = {{The rigidity theorems for complete self-expander of mean curvature flow}},
author = {Zhi Li and Guoxin Wei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20429},
eprint = {2609.20429},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20429},
note = {CC0},
}
RIS
TY - UNPB
TI - The rigidity theorems for complete self-expander of mean curvature flow
AU - Zhi Li
AU - Guoxin Wei
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.20429
UR - https://arxiv.org/abs/2609.20429
AB - Our first main result is a rigidity theorem for complete self-expanders in the Euclidean space with higher codimension, assuming an integral cur More precisely, any smooth complete self-expander x:M→ ℝ^n+p(n≥3) that satisfies both (∫_M|A|^ndμ)^1/n<K(n) and ∫_M|A|^ne^|x|^2/2dμ<∞ for a positive constant K(n) depending only o isometric to ℝ^n. Moreover, we show that the rigidity result persists when the pinching condition is expressed in terms of the trace-free second fundamental form.
ER -