My research interests lie in geometric analysis. Specifically, I study the mean curvature flow and gluing constructions for elliptic and parabolic equation but I am also interested in other geometric evolution equations (Ricci flow, inverse mean curvature flow,...), minimal surfaces, and free boundary problems. In general, I enjoy problems involving geometry and partial differential equations.
The picture on the left is a knitted Scherk surface. I created a webpage with the pattern (no seaming!) and a brief intro to the Scherk surface and other minimal surfaces.
- Negative curvature annihilates the fundamental gap of convex domains (with G. Khan)
- Log-concavity and fundamental gaps on surfaces of positive curvature (with G. Khan, M. Tuerkoen, G. Wei)
- The fundamental gap of horoconvex domains in H^n (with A. Stancu, G. Wei)
- The vanishing of the fundamental gap of convex domains in H^n (with T. Bourni, J. Clutterbuck, A. Stancu, G. Wei, V. Mira-Wheeler)
- Shrinking doughnuts via variational methods (with G. Drugan). Journal of Geometric Analysis.
- Finite topology self-translating surfaces for the mean curvature flow (with Juan Davila and Manuel Del Pino). Advances in Mathematics.
- Mean curvature flow of entire graphs evolving away from the heat flow (with G. Drugan). Proceedings of the AMS 145 (2017), pp. 861-869.
- Construction of complete embedded self-similar surfaces under mean curvature flow. Part III. Duke Mathematical Journal, August 2014, Volume 163, number 11, pp 2023-2056
- Complete embedded self-translating surfaces under mean curvature flow. Journal of Geometric Analysis, July 2013, Volume 23, Issue 3, pp 1379-1426