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Comparison Geometry for Integral Radial Bakry-Émery Ricci Tensor Bounds
In this paper we prove mean curvature comparisons and volume comparisons on a smooth metric measure space when the integral radial Bakry-Émery Ricci...
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A Sufficient Condition to a Regular Set Being of Positive Measure on Spaces
In this paper, we study regular sets in metric measure spaces with Ricci curvature bounded from below. We prove that the existence of a point in the...
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Volume Growth of Shrinking Gradient Ricci-Harmonic Soliton
In this paper, we study the shrinking gradient Ricci-harmonic soliton. Firstly using Chow–Lu–Yang’s argument, we give a necessary and sufficient...
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Bach-flat noncompact steady quasi-Einstein manifolds
The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady...
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Complete spacelike submanifolds with parallel mean curvature vector in a semi-Euclidean space
Our aim in this article is to study the geometry of n -dimensional complete spacelike submanifolds immersed in a semi-Euclidean space
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Upper Bounds for the First Eigenvalue of a Jacobi Type Operator Via Anisotropic Mean Curvatures
Our purpose in this article is to obtain sharp upper estimates for the first positive eigenvalue of a Jacobi type operator, which is a suitable...
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Isometric embeddings of 2-spheres into Schwarzschild manifolds
Let g be a Riemannian metric on the 2-sphere S 2 . Results on isometric embeddings of ( S 2 , g ) into a fixed model manifold often have implications in...
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Remarks on critical point metrics of the total scalar curvature functional
The aim of this short note is to study the space of metrics with constant scalar curvature satisfying the critical point equation on compact...
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Myers and Hawking Theorems: Geometry for the Limits of the Universe
It is known that the celebrated theorem by Hawking which assures the existence of a Big-Bang under physically motivated hypotheses, uses geometric...