Translator Disclaimer
december 2020 Submanifolds immersed in a warped product with density
Jogli G. Araújo, Henrique F. de Lima, Wallace F. Gomes, Marco Antonio L. Velásquez
Bull. Belg. Math. Soc. Simon Stevin 27(5): 683-696 (december 2020). DOI: 10.36045/j.bbms.200126

Abstract

We study $n$-dimensional complete submanifolds immersed in a weighted warped product of the type $I\times_fM^{n+p}_{\varphi}$, whose warping function $f$ has convex logarithm and weight function $\varphi$ does not depend on the real parameter $t\in I$. Assuming the constancy of an appropriate support function involving the $\varphi$-mean curvature vector field of such a submanifold $\Sigma^n$ jointly with suitable constraints on the Bakry-Émery-Ricci tensor of $\Sigma^n$, we prove that it must be contained in a slice of the ambient space. As applications, we obtain codimension reductions and Bernstein-type results for complete $\varphi$-minimal bounded multi graphs constructed over the $n$-dimensional Gaussian space. Our approach is based on the weak Omori-Yau's generalized maximum principle and Liouville-type results for the drift Laplacian.

Citation

Download Citation

Jogli G. Araújo. Henrique F. de Lima. Wallace F. Gomes. Marco Antonio L. Velásquez. "Submanifolds immersed in a warped product with density." Bull. Belg. Math. Soc. Simon Stevin 27 (5) 683 - 696, december 2020. https://doi.org/10.36045/j.bbms.200126

Information

Published: december 2020
First available in Project Euclid: 24 December 2020

MathSciNet: MR4194217
Digital Object Identifier: 10.36045/j.bbms.200126

Subjects:
Primary: 53A07, 53C42

Rights: Copyright © 2020 The Belgian Mathematical Society

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.27 • No. 5 • december 2020
Back to Top