Geometric analysis, differential geometry, partial differential equations, geometric flows, and geometric measure theory.
- Null mean curvature flow and outermost MOTS. J. Differential Geom. 111 (2019), no. 2, 191-239. With Kristen Moore.
- 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 C1,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.
- C1,α-regularity for surfaces with H in Lp. 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.
- C1,α theory for the prescribed mean curvature equation with Dirichlet data. Journal of Geometric Analysis, 21 (4), 982–1035, 2011.
- Convex ancient solutions to mean curvature flow. Differential Geometry in the Large (London Mathematical Society Lecture Note Series)}. Cambridge University Press. With Mat Langford and Giuseppe Tinaglia.
Explicit fundamental gap estimates for some convex domains in $\mathbb H^2$'. Mathematical Research Letters (to appear). With Julie Clutterbuck, Xuan Hien Nguyen, Alina Stancu, Guofang Wei and Valentina-Mira Wheeler.
- Differential Harnack inequalities via concavity of the arrival time’. Communications in Analysis and Geometry (to appear). With Mat Langford.
- Convex ancient solutions to curve shortening flow. Calculus of Variations and Partial Differential Equations, no. 4, Paper No. 133, 15pp, 202.
- Collapsing ancient solutions of mean curvature flow. Journal of Differential Geometry (to appear). With Mat Langford and Giuseppe Tinaglia.
- On the construction of closed nonconvex nonsoliton ancient mean curvature flows. International Mathematical Research Notices, Volume 2021, Issue 1, January 2021, Pages 754–765. With Mat Langford and Alexander Mramor.
- On the existence of translating solutions of mean curvature flow in slab regions. Analysis and PDE, 13-4, 1051--1072, 2020. With Mat Langford and Giuseppe Tinaglia.
- Mean Curvature Flow: Proceedings of the John H. Barrett Memorial Lectures held at the University of Tennessee, Knoxville, May 29--June 1, 2018, editor with Mat Langford, De Gruyter, Berlin (2020), 232pp.
Minimal Surfaces and the Bernstein Theorem. Book chapter co-authored with Giuseppe Tinaglia. Geometry in Advanced Pure Mathematics, 167--191, LTCC Adv. Math. Ser., 4, World Sci. Publ., Hackensack, NJ, 2017.