Related papers: A Property of K\"{a}hler-Ricci Solitons on Complet…

In this paper, by limiting twisted conical K\"ahler-Ricci flows, we prove the long-time existence and uniqueness of cusp K\"ahler-Ricci flow on compact K\"ahler manifold $M$ which carries a smooth hypersurface $D$ such that the twisted…

We address some aspects of four dimensional chiral N=1 supersymmetric theories on which the scalar manifold is described by K\"ahler geometry and can further be viewed as K\"ahler-Ricci soliton generating a one-parameter family of K\"ahler…

We prove that the Gromov-Hausdorff limit of K\"ahler-Ricci flow on a $\mathbf G$-spherical Fano manifold $X$ is a $\mathbf G$-spherical $\mathbb Q$-Fano variety $X_{\infty}$, which admits a (singular) K\"ahler-Ricci soliton. Moreover, the…

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which…

We show the properties of the blowup limits of \KRf solutions on Fano surfaces if Riemannian curvature is unbounded. As an application, on every toric Fano surface, we prove that \KRf converges to a K\"ahler Ricci soliton metric if the…

Yau's uniformization conjecture states: a complete noncompact K\"ahler manifold with positive holomorphic bisectional curvature is biholomorphic to $\ce^n$. The K\"ahler-Ricci flow has provided a powerful tool in understanding the…

In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type lower bound. As an application, we prove that compact three dimensional non-collapsed strong Kato limit space is…

In this paper, we show that the uniform L^4-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular transverse Fano Sasakian (2n+1)-manifold M. When M is dimension up to seven and the space of leaves…

We show that a simply-connected closed four-dimensional Ricci flow whose Ricci curvature is uniformly bounded below and whose volume does not approach zero must converge to a $C^{0}$ orbifold at any finite-time singularity, so has an…

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with…

In this article, we study the higher-order regularity of the K\"ahler-Ricci flow on compact K\"ahler manifolds with semi-ample canonical line bundle. We proved, using a parabolic analogue of Hein-Tosatti's work on collapsing Calabi-Yau…

We study higher-order curvature estimates along K\"ahler-Ricci flows on compact K\"ahler manifolds of intermediate Kodaira dimension. We prove that away from singular fibers, the Ricci curvature is uniformly bounded in $C^1$, the Laplacian…

In this paper we study the pseudolocality theorems of Ricci flows on incomplete manifolds. We prove that if a ball with its closure contained in an incomplete manifold has the small scalar curvature lower bound and almost Euclidean…

We show that for any solution to the K\"ahler-Ricci flow with positive bisectional curvature on a compact K\"ahler manifold $M^n$, the bisectional curvature has a uniform positive lower bound. As a consequence, the solution converges…

We show that the twisted K\"ahler-Ricci flow on a complex manifold X converges to a flow of moving free boundaries, in a certain scaling limit. This leads to a new phenomenon of singularity formation and topology change which can be seen as…

This paper is concerned with properties of maximal solutions of the Ricci and cross curvature flows on locally homogeneous three-manifolds of type SL(2,R). We prove that, generically, a maximal solution originates at a sub-Riemannian…

We prove two rigidity theorems for open (complete and noncompact) $n$-manifolds $M$ with nonnegative Ricci curvature and the infimum of volume growth order $<2$. The first theorem asserts that the Riemannian universal cover of $M$ has…

Recently it has been proved (Lee-Topping 2022, Deruelle-Schulze-Simon 2022, Lott 2019) that three-dimensional complete manifolds with non-negatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton.…

We consider the K\"ahler-Ricci flow $(X, \omega(t))_{t \in [0,T)}$ on a compact manifold where the time of singularity, $T$, is finite. We assume the existence of a holomorphic map from the K\"ahler manifold $X$ to some analytic variety $Y$…

In this paper we study volume growth of gradient steady Ricci solitons. We show that if the potential function satisfies a uniform condition, then the soliton has at most Euclidean volume growth.