Rigidity Results for Spacelike Self-Shrinkers via Different Maximum Principles

2025/08/17 by Barboza, Weiller F. Chaves
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.12196

Abstract

In this work, we establish several rigidity results for spacelike self-shrinkers immersed in the pseudo-Euclidean space ℝ^n+p_p. Under suitable boundedness conditions on either the mean curvature vector or the second fundamental form, we apply different versions of Omori--Yau type maximum principles due to Qiu [20], Chen and Qiu [10], and Alías, Caminha, and Nascimento [3] to show that such self-shrinkers must be spacelike hyperplanes. These results contribute to the broader classification of spacelike self-shrinkers under natural geometric assumptions.

Citations

• Spacelike Self-Similar Shrinking Solutions of the Mean Curvature Flow in Pseudo-Euclidean Spaces
• Some results on space-like self-shrinkers
• The rigidity theorems for Lagrangian self shrinkers
• A Gap Theorem for Self-shrinkers of the Mean Curvature Flow in Arbitrary Codimension
• Rigidity of Entire self-shrinking solutions to curvature flows
• A Bernstein Type Theorem For Self-similar Shrinkers
• Generic mean curvature flow I; generic singularities
• Translating solutions to Lagrangian mean curvature flow
• Convex solutions to the mean curvature flow
• Some aspects of the global geometry of entire space-like submanifolds

Related

• The rigidity theorems of self shrinkers
• Some results on space-like self-shrinkers
• A maximum principle for self-shrinkers and some consequences
• The rigidity theorem for complete Lagrangian self-shrinkers
• Complete self-shrinkers of the mean curvature flow