Results 11 to 20 of about 1,067 (29)

On the lower bound of the K energy and F functional [PDF]

, 2008
Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.Comment: Final version, to appear in Osaka Journal of ...
Li, Haozhao
core   +2 more sources

A survey on Inverse mean curvature flow in ROSSes

Complex Manifolds, 2017
In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces.
Pipoli Giuseppe
doaj   +1 more source

A new proof of the bound for the first Dirichlet eigenvalue of the Laplacian operator

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
In this paper, we present a new proof of the upper and lower bound estimates for the first Dirichlet eigenvalue λ1D(B(p,r))$\lambda _1^D \left({B\left({p,r} \right)} \right)$ of Laplacian operator for the manifold with Ricci curvature Rc ≥ −K, by using
Li Chang-Jun, Gao Xiang
doaj   +1 more source

A Remark on Soliton Equation of Mean Curvature Flow

, 2003
In this short note, we consider self-similar immersions $F: \mathbb{R}^n \to \mathbb{R}^{n+k}$ of the Graphic Mean Curvature Flow of higher co-dimension.
Ma, L., Yang, Y.
core   +5 more sources

A simple proof of the short-time existence and uniqueness for Ricci flow

, 2018
In this short note we give a simple proof for the local existence and uniqueness for the Ricci flow on a compact manifold.
Eftekharinasab, Kaveh
core   +1 more source

Curvature conditions, Liouville-type theorems and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces

Advanced Nonlinear Studies
In this paper we prove gradient estimates of both elliptic and parabolic types, specifically, of Souplet-Zhang, Hamilton and Li-Yau types for positive smooth solutions to a class of nonlinear parabolic equations involving the Witten or drifting Laplacian
Taheri Ali, Vahidifar Vahideh
doaj   +1 more source

Riemann Solitons on Homogeneous Siklos Spacetimes

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we investigate the properties of Riemann solitons on homogeneous Siklos spacetimes. Siklos spacetimes, which are special solutions to Einstein’s equations with a wave‐like potential, provide a suitable setting for studying the geometric properties of Riemann solitons.
Mehdi Jafari, Amirhesam Zaeim, Adele Alemahdi, Erhan Güler   +3 more
wiley   +1 more source

2‐Conformal Vector Fields on the Model Sol Space and Hyperbolic Ricci Solitons

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this study, we present the notion of 2‐conformal vector fields on Riemannian and semi‐Riemannian manifolds, which are an extension of Killing and conformal vector fields. Next, we provide suitable vector fields in Sol space that are 2‐conformal. A few implications of 2‐conformal vector fields in hyperbolic Ricci solitons are investigated.
Rawan Bossly, Ghodratallah Fasihi-Ramandi, Mohd Danish Siddiqi, Antonio Masiello   +3 more
wiley   +1 more source

Sharp Entropy Bounds for Self-Shrinkers in Mean Curvature Flow

, 2018
Let $M\subset {\mathbf R}^{m+1}$ be a smooth, closed, codimension-one self-shrinker (for mean curvature flow) with nontrivial $k^{\rm th}$ homology. We show that the entropy of $M$ is greater than or equal to the entropy of a round $k$-sphere, and that ...
Hershkovits, Or, White, Brian
core   +1 more source

Asymptotically Hyperbolic Metrics on Unit Ball Admitting Multiple Horizons

, 2007
In this paper, we construct an asymptotically hyperbolic metric with scalar curvature -6 on unit ball $\mathbf{D}^3$, which contains multiple horizons.Comment ...
Li, ZhenYang, Shi, YuGuang, Wu, Peng
core   +1 more source