Stability properties and topology at infinity of $$f$$ f -minimal hypersurfaces

Impera, Debora; Rimoldi, Michele

doi:10.1007/s10711-014-9999-6

Cited by 54 publications

(41 citation statements)

References 42 publications

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“…Remark 2 As it was observed by Impera and Rimoldi in Remark 3 of Impera and Rimoldi (2014), a sufficient condition for a weighted manifold n f to be f -parabolic is that it is geodesically complete and…”

Section: Key Lemmasmentioning

confidence: 83%

Rigidity of complete spacelike hypersurfaces with constant weighted mean curvature

2015

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Our aim in this article is to study the rigidity of complete spacelike hypersurfaces immersed in a weighted Lorentzian product space of the type R 1 × P n f , whose Bakry-Émery-Ricci tensor of the fiber P n is nonnegative and the Hessian of the weighted function f is bounded from below. In this setting, supposing that the weighted mean curvature H f is constant and assuming appropriated constraints on the norm of the gradient of the height function, we prove that such a hypersurface must be a slice of the ambient space. Applications to entire spacelike graphs construct over P n are also given. Our approach is based on a suitable formula for the drift Laplacian of an angle function naturally attached to a spacelike hypersurface jointly with a weak version of the Omori-Yau's generalized maximum principle.

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Section: Key Lemmasmentioning

confidence: 83%

Rigidity of complete spacelike hypersurfaces with constant weighted mean curvature

2015

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“…simply connected, with nonpositive sectional curvature), and that, setting η =η • ψThen, every end of M is ∆ −cη -hyperbolic.Proof. The proof directly follows from results in[IR15], so we will be sketchy. −cη the (m−1)-dimensional measure weighted by e cη , and ∂B r (x) the sphere in the metric of M .Therefore, M enjoys the Sobolev inequality in [IR15, Thm.…”

mentioning

confidence: 95%

Remarks on mean curvature flow solitons in warped products

Colombo¹,

Mari²,

Rigoli³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces. We focus on splitting and rigidity results under various geometric conditions, ranging from the stability of the soliton to the fact that the image of its Gauss map be contained in suitable regions of the sphere. We also investigate the case of entire graphs.

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“…We were informed of an independent manuscript of Impera and Rimoldi [17] which proves a similar version of Theorem 1 for the case that M is a hypersurface in a weighted manifold M with nonpositive sectional curvature. The authors thank them for useful comments.…”

Section: Theorem 2 Assume Thatm Satisfiesmentioning

confidence: 99%