A weighted volume estimate and its application to Bernstein type theorems in Gauss space
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 25-28
MSC: Primary 53C42; Secondary 53C50, 53C25.
DOI: 10.4064/cm7562-11-2018
Published online: 20 September 2019
Abstract
A weighted area estimate for entire graphs with bounded weighted mean curvature in a Gauss space is given, with a short proof. Bernstein type theorems for self-shrinkers (Wang, 2011) as well as for graphic $\lambda $-hypersurfaces (Cheng and Wei, 2014) are immediate consequences.
