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

Junior Tavares; Detang Zhou

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arXiv · 2609.26559

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

Junior Tavares·Detang Zhou

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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.

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BibTeX RIS

Junior Tavares, Detang Zhou. 2026-09-22. Volume Growth of Self-Shrinkers of the $Q_k$-Flow in $\mathbb{R}^{n+1}$. https://arxiv.org/abs/2609.26559

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