## 731 Citations

SO(2) Symmetry of the Translating Solitons of the Mean Curvature Flow in
$$\mathbb {R}^4$$
R
4

- MathematicsAnnals of PDE
- 2022

In this paper, we prove that the translating solitons of the mean curvature flow in $$\mathbb {R}^4$$ R 4 which arise as blow-up limit of embedded, mean convex mean curvature flow must have SO (2)…

Classification of Ricci solitons

- Mathematics
- 2020

There are two important aspects of Ricci solitons. One looking at the influence on the topology by the Ricci soliton structure of the Riemannian manifold, and the other looking at its influence in…

Hermitian curvature flow on complex homogeneous manifolds

- MathematicsANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- 2020

In this paper we study a version of the Hermitian curvature flow (HCF). We focus on complex homogeneous manifolds equipped with induced metrics. We prove that this finite-dimensional space of metrics…

The Hermitian curvature flow on manifolds with non-negative Griffiths curvature

- MathematicsAmerican Journal of Mathematics
- 2019

Abstract:In this paper we study a particular version of the {\it Hermitian curvature flow} (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths…

Classification of Gradient Shrinking Ricci Solitons

- Mathematics
- 2018

There are two important aspects of Ricci solitons. One looks at the influence on the topology by the Ricci solitons structure of the Riemannian manifold, and the other looks at its geometric…

Lie-algebraic curvature conditions preserved by the Hermitian curvature flow

- Mathematics
- 2017

The purpose of this paper is to prove that the Hermitian Curvature Flow (HCF) on an Hermitian manifold ( M , g , J ) preserves many natural curvature positivity conditions. Following ideas of…

Characterizations of the compactness of Riemannian manifolds by eigenfunctions, and a partial proof of a conjecture by Hamilton

- Mathematics
- 2016

In this paper, we deal with comparison theorems for the first eigenvalue of the Schrödinger operator, and we present some criteria for the compactness of a Riemannian manifold in terms of the…

SOME PARABOLIC AND ELLIPTIC PROBLEMS IN COMPLEX RIEMANNIAN GEOMETRY

- Mathematics
- 2015

OF THE DISSERTATION Some parabolic and elliptic problems in complex Riemannian geometry by Bin Guo Dissertation Director: Professor Jian Song This dissertation consists of three parts, the first one…

Bernstein theorems for length and area decreasing minimal maps

- Mathematics
- 2014

In this article we prove Liouville and Bernstein theorems in higher codimension for length and area decreasing maps between two Riemannian manifolds. The proofs are based on a strong elliptic maximum…

Local smoothing results for the Ricci flow in dimensions two and three

- Mathematics
- 2013

We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality…