## Research papers

### Under review

- Harnack inequalities for the curve shortening flow. Preprint
*submitted*

### Published or accepted for publication

- A Harnack inequality for the parabolic Allen-Cahn equation. Preprint
*Annals of Global Analysis and Geometry*
- (with H. Tran) Heat kernel estimates under the Ricci-Harmonic Map flow. Preprint
*to appear in* Proceedings of the Edinburgh Mathematical Society
- Gradient estimates for the heat equation under the Ricci-Harmonic Map flow., Preprint
*Advances in Geometry*, 15(4):445–454, 2015
- Bounds on the heat kernel under the Ricci flow.
*Proc. of the AMS *, 140:691-700, 2012 Preprint
- (with X. Cao and A. Pulemotov) Gradient estimates for the heat equation under the Ricci flow.
*J. Funct. Anal.*, 258(10):3517-3542, 2010 Preprint
- (with V. Balan and D. Schleicher) Hausdorff dimension of exponential parameter rays and their endpoints.
*Nonlinearity*, 11(1):113-120, 2008 Preprint