Research Interests
Geometric analysis, differential geometry, partial differential equations, geometric flows, and geometric measure theory.
Publications
- On the existence of translating solutions of mean curvature flow in slab regions. Analysis and PDE (to appear). With Mat Langford and Giuseppe Tinaglia.
- Null mean curvature flow and outermost MOTS. J. Differential Geom. 111 (2019), no. 2, 191-239. With Kristen Moore.
- Minimal surfaces and the Bernstein theorem. Geometry in Advanced Pure Mathematics, 167–191, LTCC Adv. Math. Ser., 4, World Sci. Publ., Hackensack, NJ,2017. With Giuseppe Tinaglia.
- Type-II singularities of two-convex immersed mean curvature flow. Geometric Flows (2), 1–17, 2016. With Mat Langford
- An Allard type regularity theorem for varifolds with a Hölder condition on the first variation. Calculus of Variations and Partial Differential Equations, 55: 46, 2016. With Alex Volkmann.
- Allard-type boundary regularity for C^{1,α} boundaries. Advances in Calculus of Variations, 9 (2), 143–161, 2016.
- Area minimizing surfaces in mean convex 3-manifolds. Journal für die Reine und Angewandte Mathematik, 704, 135–167, 2015. With Baris Coskunuzer.
- C^{1,α}-regularity for surfaces with H in L^{p}. Annals of Global Analysis and Geometry, 46 (2), 159–186, 2014. With Giuseppe Tinaglia
- Density estimates for compact surfaces with total boundary curvature less than 4π. Communications in Partial Differential Equations, 37 (10–12), 1870–1886, 2012. With Giuseppe Tinaglia.
- Curvature estimates for surfaces with bounded mean curvature. Transactions of the American Mathematical Society, 364 (11), 5813–5828, 2012. With Giuseppe Tinaglia.
- C^{1,α} theory for the prescribed mean curvature equation with Dirichlet data. Journal of Geometric Analysis, 21 (4), 982–1035, 2011.
Preprints