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A weighted volume estimate and its application to Bernstein type theorems in Gauss space

Volume 159 / 2020

Doan The Hieu Colloquium Mathematicum 159 (2020), 25-28 MSC: Primary 53C42; Secondary 53C50, 53C25. DOI: 10.4064/cm7562-11-2018 Published online: 20 September 2019


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.


  • Doan The HieuCollege of Education
    Hue University
    32 Le Loi, Hue, Vietnam

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