Work

Volume Growth of Self-Shrinkers of the $Q_k$-Flow in $\mathbb{R}^{n+1}$

Year: 2026

Type: preprint

Abstract: In this paper, we establish a general volume estimate for complete Riemannian manifolds under suitable differential inequalities involving a proper function and a symmetric tensor, without imposing curvature assumptions. As an application, we prove that a class of orientable hypersurfaces properly immersed in Euclidean space has at most polynomial volume growth and finite weighted volume. This class includes, in particular, certain self-shrinkers of the $Q_k$-flow and properly immersed minimal hypersurfaces for which the normal component of the position vector is bounded.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.26559

Authors: Tavares, Junior, Zhou, Detang

Institution: Universidade Federal Fluminense

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico

OpenAlex ID: W7214096577

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