The Equality case in the substatic Heintze–Karcher inequality
We provide a rigidity statement for the equality case of the Heintze–Karcher inequality in
substatic manifolds. We apply such a result in the warped product setting to fully remove …
substatic manifolds. We apply such a result in the warped product setting to fully remove …
Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with -range
Y Fujitani - manuscripta mathematica, 2024 - Springer
For n-dimensional weighted Riemannian manifolds, lower m-Bakry–Émery–Ricci curvature
bounds with ε-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10 (1): 1 …
bounds with ε-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10 (1): 1 …
Some splitting and rigidity results for sub-static spaces
In this paper we study the rigidity problem for sub-static systems with possibly non-empty
boundary. First, we get local and global splitting theorems by assuming the existence of …
boundary. First, we get local and global splitting theorems by assuming the existence of …
Willmore-type inequalities for closed hypersurfaces in weighted manifolds
G Wu, JY Wu - arxiv preprint arxiv:2404.16286, 2024 - arxiv.org
In this paper, we prove some Willmore-type inequalities for closed hypersurfaces in
weighted manifolds with nonnegative Bakry-\'Emery Ricci curvature. In particular, we give a …
weighted manifolds with nonnegative Bakry-\'Emery Ricci curvature. In particular, we give a …
Uniqueness of equipotential photon surfaces in 4-dimensional static vacuum asymptotically flat spacetimes for positive, negative, and zero mass--and a new partial …
C Cederbaum, A Cogo, A Fehrenbach - arxiv preprint arxiv:2407.21522, 2024 - arxiv.org
We present different proofs of the uniqueness of 4-dimensional static vacuum asymptotically
flat spacetimes containing a connected equipotential photon surface or in particular a …
flat spacetimes containing a connected equipotential photon surface or in particular a …
Riccati Equation for Static Spaces and its Applications
Z Wang - arxiv preprint arxiv:2408.12180, 2024 - arxiv.org
In this paper, we derive a Riccati-type equation applicable to (sub-) static Einstein spaces
and examine its various applications. Specifically, within the framework of conformally …
and examine its various applications. Specifically, within the framework of conformally …