相关论文: Geometric formalities along the Chern-Ricci flow
A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman along with earlier work of Boileau-Leeb-Porti and Cooper-Hodgson-Kerckhoff. We give a new, logically…
By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
In this paper we establish partial structure results on the geometry of compact Hermitian manifolds of semipositive Griffiths curvature. We show that after appropriate arbitrary small deformation of the initial metric, the null spaces of…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation…
We introduce a new geometric flow of Hermitian metrics which evolves an initial metric along the second derivative of the Chern scalar curvature. The flow depends on the choice of a background metric, it always reduces to a scalar equation…
In 1974, S.-S. Chern and J. Simons published a paper where they defined a new type of characteristic class - one that depends not just on the topology of a manifold but also on the geometry. The goal of this paper is to investigate what…
Giving explicit parametrizations of discrete constant Gaussian curvature surfaces of revolution that are defined from an integrable systems approach, we study Ricci flow for discrete surfaces, and see how discrete surfaces of revolution…
We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
We study deformations of Riemannian metrics on a given manifold equipped with a codimension-one foliation subject to quantities expressed in terms of its second fundamental form. We prove the local existence and uniqueness theorem and…
We consider the holographic renormalization group (RG) flow in three dimensional gravity with the gravitational Chern-Simons term coupled to some scalar fields. We apply the canonical approach to this higher derivative case and employ the…
For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collapsing and non-inflated properties, which generalize the…
The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential…
We study the Hermitian curvature flow of locally homogeneous non-K\"ahler metrics on compact complex surfaces. In particular, we characterize the long-time behavior of the solutions to the flow. We also provide the first example of a…
We construct a class of Riemannian metrics in closed surfaces of genus greater than one, having Anosov geodesic flows, and some regions of positive curvature, such that for each such surface, there exists a smooth curve of conformal…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the…
In Part I, we develop the notions of a Moebius structure and a conformal Cartan geometry, establish an equivalence between them; we use them in Part II to study submanifolds of conformal manifolds in arbitrary dimension and codimension. We…