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Spacelike mean curvature flow solitons in standard static spacetimes and new Calabi–Bernstein type results
We investigate solitons of the spacelike mean curvature flow with respect to the timelike Killing vector field of a standard static spacetime. In...
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Spacelike mean curvature flow solitons, polynomial volume growth and stochastic completeness of spacelike hypersurfaces immersed into pp-vave spacetimes
Our purpose in this paper is to study some geometric properties of spacelike hypersurfaces immersed into a pp-wave spacetime , namely, a connected...
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Nonexistence and rigidity of spacelike mean curvature flow solitons immersed in a GRW spacetime
We study the nonexistence and rigidity of an important class of particular cases of trapped submanifolds, more precisely, n -dimensional spacelike...
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Rigidity of Mean Curvature Flow Solitons and Uniqueness of Solutions of the Mean Curvature Flow Soliton Equation in Certain Warped Products
We obtain rigidity results concerning complete noncompact mean curvature flow solitons immersed in certain semi-Riemannian warped products, under...
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Classification of Ruled Surfaces as Homothetic Self-Similar Solutions of the Inverse Mean Curvature Flow in the Lorentz–Minkowski 3-Space
In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz–Minkowski space that are homothetic self-similar...
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Snapshots of Non-local Constrained Mean Curvature-Type Flows
The mean curvature flow is the most natural way to deform a hypersurface according to its curvature, since it evolves the parametrization by means of...
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Ricci Solitons on Riemannian Hypersurfaces Arising from Closed Conformal Vector Fields in Riemannian and Lorentzian Manifolds
This paper investigates Ricci solitons on Riemannian hypersurfaces in both Riemannian and Lorentzian manifolds. We provide conditions under which a...
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Singularities of mean curvature flow
Mean curvature flow and its singularities have been paid attention extensively in recent years. The present article reviews briefly their certain...
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Translating Solutions of the Nonparametric Mean Curvature Flow with Nonzero Neumann Boundary Data in Product Manifold Mn × ℝ
In this paper, the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary...
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Self-similar solutions to the curvature flow and its inverse on the 2-dimensional light cone
We consider a novel curvature flow for curves on the 2-dimensional light cone, contained in the 3-dimensional Minkowski space. We show that the...
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Generalized Yamabe solitons on hypersurfaces in pseudo–Euclidean spaces
In this paper, we obtain a classification theorem for generalized Yamabe solitons, called conformal solitons, on pseudo–Riemannian hypersurfaces in...
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Translating Surfaces of the Non-parametric Mean Curvature Flow in Lorentz Manifold M2 × ℝ*
In this paper, for the Lorentz manifold M 2 × ℝ with M 2 a 2-dimensional complete surface with nonnegative Gaussian curvature, the authors investigate...
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A Rigidity Result of Spacelike Self-Shrinkers in Pseudo-Euclidean Spaces
In this paper, the author proves that the spacelike self-shrinker which is closed with respect to the Euclidean topology must be flat under a growth...
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Generalized Wintgen Inequalities for \((\epsilon )\) -Para Sasakian Manifold
This study explores generalized Wintgen inequalities for a contact pseudo-slant submanifold of...