Some maximum principles for the drift Laplacian applied to complete spacelike hypersurfaces

Danilo F. Silva (), Eraldo A. Lima () and Henrique F. Lima ()
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Danilo F. Silva: Universidade Federal da Paraíba
Eraldo A. Lima: Universidade Federal da Paraíba
Henrique F. Lima: Universidade Federal de Campina Grande

Partial Differential Equations and Applications, 2023, vol. 4, issue 2, 1-16

Abstract: Abstract Under suitable constraints on the Bakry–Émery–Ricci tensor and on the norm of the gradient of the height function, we apply some maximum principles related to the drift Laplacian in weighted Riemannian manifolds to study the uniqueness of complete spacelike hypersurfaces immersed with constant f-mean curvature in a weighted Lorentzian product space of the type $$-{{\mathbb {R}}}\times M^n_f.$$ - R × M f n . New Calabi–Bernstein type results concerning spacelike entire graphs defined on the Riemannian base $$M^n$$ M n are also given.

Keywords: Drift Laplacian; Lorentzian product spaces; Bakry–Émery–Ricci tensor; Complete spacelike hypersurfaces; Calabi–Bernstein type results; Primary 53C42; Secondary 53B30; 53C50 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-022-00221-z

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