arXiv subjects

Yuanqi Wang

Publications and source records attributed to Yuanqi Wang.

22 records · Page 2Linked to original sources

arXiv2013

On the Kähler-Ricci flow near a Kähler-Einstein metric

On a Fano manifold, we prove that the Kahler-Ricci flow starting from a Kahler metric in the anti-canonical class which is sufficiently close to a Kahler-Einstein metric must converge in a polynomial rate to a Kahler-Einstein metric. The convergence can not happen in general if we study the flow on the level of Kahler potentials. Instead we exploit the interpretation of the Ricci flow as the gradient flow of Perelman's μfunctional. This involves modifying the Ricci flow by a canonical family of gauges. In particular, the complex structure of the limit could be different in general. The main technical ingredient is a Lojasiewicz type inequality for Perelman's μfunctional near a critical point.

math.DG↗

arXiv2011

On four-dimensional anti-self-dual gradient Ricci solitons

In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons with bounded curvature.

math.DG↗

arXiv2009

Pseudolocality of Ricci Flow under Integral Bound of Curvature

We prove a pseudolocality type theorem for compact Ricci Flow under local integral bounds of curvature. The main tool is Local Ricci Flow introduced by Deane Yang in [4] and Pseudolocality Theorem of Perelman in [3]. We also study L^p bounds for the derivatives of curvature and smooth extension of Local Ricci Flow.

math.DG↗

arXiv2008

A New Ricci Flow Proof of Frankel Conjecture

The aim of this paper is to give a proof the Frankel conjecture by using the Kahler Ricci flow alone without assuming apriori the existence of Kahler Einstein metrics. However, there is an essential difference between the real case and the Kahler case. I didn't realize this difference in the calculation of the previous version thus made a mistake on the crucial point.

math.DG↗