## 2,558 Citations

Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I

- Mathematics
- 2022

A bstract . We extend Cheeger-Gromov’s and Anderson’s convergence theorems to regular limit spaces of manifolds with bounded Ricci curvature and local covering geometry, by establishing the C 1 ,α…

Mean curvature flow of area decreasing maps in codimension two

- Mathematics
- 2022

We consider the graphical mean curvature flow of strictly area decreasing maps f : M → N between a compact Riemannian manifold M of dimension m > 1 and a complete Riemannian surface N of bounded…

Small curvature concentration and Ricci flow smoothing

- MathematicsJournal of Functional Analysis
- 2022

Ricci flow smoothing for locally collapsing manifolds

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

We show that for certain locally collapsing initial data with Ricci curvature bounded below, one could start the Ricci flow for a definite period of time. This provides a Ricci flow smoothing tool,…

Local curvature estimates for the Ricci-harmonic flow

- MathematicsNonlinear Analysis
- 2022

K\"ahler-Ricci flow on rational homogeneous varieties

- Mathematics
- 2021

In this work, we study the Kähler-Ricci flow on rational homogeneous varieties exploring the interplay between projective algebraic geometry and representation theory which underlies the classical…

Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry

- MathematicsCalculus of Variations and Partial Differential Equations
- 2021

We study harmonic map heat flow along ancient super Ricci flow, and derive several Liouville theorems with controlled growth from Perelman’s reduced geometric viewpoint. For non-positively curved…

The commutative nonassociative algebra of metric curvature tensors

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract The space of tensors of metric curvature type on a Euclidean vector space carries a two-parameter family of orthogonally invariant commutative nonassociative multiplications invariant with…

Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2020

We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and the Ricci flow…

Generalized Ricci Flow

- Mathematics
- 2020

This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields…

## References

SHOWING 1-5 OF 5 REFERENCES

Spaces of Constant Curvature

- Mathematics
- 1984

This sixth edition illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds…

Comparison theorems in Riemannian geometry

- Mathematics
- 1975

Basic concepts and results Toponogov's theorem Homogeneous spaces Morse theory Closed geodesics and the cut locus The sphere theorem and its generalizations The differentiable sphere theorem Complete…

Harmonic Maps of Manifolds with Boundary

- Mathematics
- 1975

Harmonic maps.- Function spaces.- Semi-elliptic and parabolic equations.- The heat equation for manifolds.- Growth estimates and convergence.