{"ID":23586791,"CreatedAt":"2026-09-18T05:25:32.833479871Z","UpdatedAt":"2026-09-18T05:25:32.833479871Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20429","arxiv_id":"2609.20429","title":"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 $x:M\\to \\mathbb R^{n+p}$($n\\geq3$) that satisfies both $(\\int_{M}|A|^{n}dμ)^{\\frac{1}{n}}\u003cK(n)$ and $\\int_{M}|A|^{n}e^{\\frac{|x|^{2}}{2}}dμ\u003c\\infty$ for a positive constant $K(n)$ depending only o isometric to $\\mathbb R^{n}$. Moreover, we show that the rigidity result persists when the pinching condition is expressed in terms of the trace-free second fundamental form.","short_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 $x:M\\to \\mathbb R^{n+p}$($n\\geq3$) that satisfies both $(\\int_{M}|A|^{n}dμ)^{\\frac{1}{n}}\u003cK(n)$ and $\\int_{M}|A|^{n}e^{\\frac{...","url_abs":"https://arxiv.org/abs/2609.20429","url_pdf":"https://arxiv.org/pdf/2609.20429v1","authors":"[\"Zhi Li\",\"Guoxin Wei\"]","published":"2026-09-17T14:09:15Z","proceeding":"math.DG","tasks":"[\"math.DG\"]","methods":"[]","has_code":false}