Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 42 min ago
PreprintarXiv licencearXiv

Volume Growth of Self-Shrinkers of the Qk-Flow in ℝn+1

  • Junior Tavares
  • Detang Zhou
Open at sourcePDFDOICite

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 Qk-flow and properly immersed minimal hypersurfaces for which the normal component of the position vector is bounded.

Related

  1. Foliation by bi-rotational self shrinkers in Euclidean space
    Junyoung Park
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  2. Complete self-shrinkers with constant norm of the second fundamental form in RR4
    Yu Fu, Dan Yang
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. Rigidity of Three-Dimensional Self-Shrinkers with Constant Norm of the Second Fundamental Form
    Shanlin Guan, Yuhang Zhao
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  4. The second gap for self-shrinkers with constant norm of the second fundamental form
    Pengpeng Cheng, Tongzhu Li
    arXivPreprintCC BY-NC-ND 4.0Full textGeometry & topologyarXiv
  5. Rigidity theorems of complete self-shrinkers in the Euclidean space
    Zhi Li, Guoxin Wei, Cheng Xing
    arXivPreprintCC0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{tavares2026volume,
  title = {{Volume Growth of Self-Shrinkers of the $Q_k$-Flow in $\mathbbR^n+1$}},
  author = {Junior Tavares and Detang Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26559},
  eprint = {2609.26559},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26559},
}
RIS
TY  - UNPB
TI  - Volume Growth of Self-Shrinkers of the Q_k-Flow in ℝ^n+1
AU  - Junior Tavares
AU  - Detang Zhou
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26559
UR  - https://arxiv.org/abs/2609.26559
AB  - 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.
ER  -