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.
- (version: November 08, 2016) Shrinking doughnuts via variational methods (with G. Drugan). Submitted to Journal of Geometric Analysis.
- (version: March 08, 2017) Iterated Routh's triangles (with E. Carroll, A. P. Ghosh, and A. Roitershtein). Accepted in the Journal for Geometry and Graphics.
- (version: January 12, 2017) Finite topology self-translating surfaces for the mean curvature flow (with Juan Davila and Manuel Del Pino). Accepted in Advances in Mathematics (August 2017).
- (version: April 07, 2016) Mean curvature flow of entire graphs evolving away from the heat flow (with G. Drugan). Proceedings of the AMS 145 (2017), pp. 861-869.
(version: June 27, 2014) Doubly periodic self-translating surfaces for the mean curvature flow.
Geometriae Dedicata 174 (2015), 177-185.
(version: July 2, 2014) Construction of Complete Embedded Self-Similar Surfaces under
Mean Curvature Flow. Part III (pdf). Duke Mathematical Journal,
August 2014, Volume 163, number 11, pp 2023-2056
Complete Embedded Self-Translating Surfaces under
Mean Curvature Flow (pdf). Journal of Geometric Analysis,
July 2013, Volume 23, Issue 3, pp 1379-1426
- A longitudinal study on students' development and transfer of the concept of integration (pdf) (with A. Bennett and T. Moore). American Society for Engineering Education Conference Proceedings, June 26-29, 2011, Vancouver, British Columbia, Canada.
- Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part II (pdf). Advances in Differential Equations, volume 15, numbers 5-6, April/May 2010.
- Translating Tridents (pdf). Comm. in Partial Differential Equations, volume 34, Issue 3 (2009), p 257-280.
- Construction of Complete Embedded Self-Similar Surfaces under Mean Curvature Flow. Part I (pdf). Trans. of the Amer. Math. Soc. 361 (2009), 1683-1701.
- Desingularization of immersed surfaces (with Stephen Kleene).
- A survey of closed self-shrinkers for the mean curvature flow (with G. Drugan and H. Lee)