Bernstein theorem for translating solitons of hypersurfaces

2014/05/13 by Li Ma, Ma, Li, M. A. Facas Vicente +1 · 1 citation
Computer Science · Engineering · Mathematics · #35Jxx #53Cxx #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1405.3042

openalex publication_date 2014/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in \reⁿ⁺¹, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap theorem for the translating soliton of hypersurfaces in R^n+k, namely, if the Lⁿ norm of the second fundamental form of the soliton is small enough, then it is a hyperplane.

Citations

• Curvature estimates for minimal hypersurfaces

Cited by

• A mean value inequality for the generalized self-expander type submanifolds and its application

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