相关论文: The Chern-Ricci flow on Oeljeklaus-Toma manifolds

We consider the Ricci flow for simply connected nilmanifolds, which translates to a Ricci flow on the space of nilpotent metric Lie algebras. We consider the evolution of the inner product and the evolution of structure constants, as well…

We introduce a flow of Riemannian metrics over compact manifolds with formal limit at infinite time a shrinking Ricci soliton. We call this flow the Soliton-Ricci flow. It correspond to a Perelman's modified backward Ricci type flow with…

We establish global existence of the pluriclosed flow with arbitrary initial data on Oeljeklaus-Toma manifolds, and Gromov-Hausdorff convergence of blowdown limits to a torus under natural conjectural bounds on the flow at infinity. In the…

The Hopf surfaces provide a family of minimal non-K\"ahler surfaces of class VII on which little is known about the Chern-Ricci flow. We use a construction of Gauduchon-Ornea for locally conformally K\"ahler metrics on primary Hopf surfaces…

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.

We show that on smooth minimal surfaces of general type, the K\"ahler-Ricci flow starting at any initial K\"ahler metric converges in the Gromov-Hausdorff sense to a K\"ahler-Einstein orbifold surface. In particular, the diameter of the…

We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general…

In this note, we prove the existence of weak solutions of the Chern-Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the exceptional curves on compact complex surfaces. The smoothing…

In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence…

We prove that a general complex Monge-Amp\`ere flow on a Hermitian manifold can be run from an arbitrary initial condition with zero Lelong number at all points. Using this property, we confirm a conjecture of Tosatti-Weinkove: the…

We establish uniform diameter estimates and volume non-collapsing estimates for the Chern-Ricci flow on smooth Hermitian minimal models of general type, assuming the initial metric is K\"ahler in a neighborhood of the null locus of the…

We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result…

Using a recently developed piecewise flat method, numerical evolutions of the Ricci flow are computed for a number of manifolds, using a number of different mesh types, and shown to converge to the expected smooth behaviour as the mesh…

Consider a sequence of pointed n-dimensional complete Riemannian manifolds {(M_i,g_i(t), O_i)} such that t in [0,T] are solutions to the Ricci flow and g_i(t) have uniformly bounded curvatures and derivatives of curvatures. Richard Hamilton…

The main objective of this thesis is the study of the evolution under the Ricci flow of surfaces with singularities of cone type. A second objective, emerged from the techniques we use, is the study of families of Ricci flow solitons in…

In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and…

We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…

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…

In this work, we first establish short time existence and Shi's type estimate of second Ricci flow on complete noncompact Hermitian manifolds. As an application, we use the second Ricci flow to discuss the existence of Kaehler-Einstein…

The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified…