Research


I am interested in nonlinear problems in differential geometry, partial differential equations, and geometric topology.

Papers


The Morse index of a minimal surface
to appear Notices Amer. Math. Soc.
(joint with O. Chodosh)

Waist inequality for 3-manifolds with positive scalar curvature
to appear in Perspectives on Scalar Curvature, World Scientific Publishing Company
(joint with Y. Liokumovich)

On the topology and index of minimal surfaces II
to appear in
J. Differential Geom. (joint with O. Chodosh)

A note on minimal surfaces with bounded index
to appear in Comm. Anal. Geom.

Minimal surfaces with bounded index
Invent. Math. 209 (2017), no. 3, 617–664. (joint with O. Chodosh and D. Ketover)

Almost-rigidity and the extinction time of positively curved Ricci flows
Math. Ann. 369 (2017), no. 1-2, 899–911. (joint with R. Bamler)

Metrics with non-negative Ricci curvature on convex three-manifolds
Geom. Topol. 20 (2016), no. 5, 2905–2922. (joint with A. Ache and H. Wu)

Free boundary minimal annuli in convex three-manifolds
J. Differential Geom. 106 (2017), no. 1, 139–186. (joint with I. Nunes and G. Smith)

On the topology and index of minimal surfaces
J. Differential Geom. 104 (2016), no. 3, 399–418 (joint with O. Chodosh)

On the blow-up of four-dimensional Ricci flow singularities
J. Reine Angew. Math. 692 (2014), 153–171.

On the Aleksandrov-Bakelman-Pucci estimate for the infinity Laplacian
Calc. Var. Partial Differential Equations 48 (2013), no. 3-4, 667–693.
(joint with F. Charro, G. De Philippis and A. Di Castro)

Hawking mass and local rigidity of minimal two-spheres in three-manifolds
Comm. Anal. Geom. 21 (2013), no. 2, 409–432. (joint with I. Nunes)

Non-negative Ricci curvature on closed manifolds under Ricci flow
Proc. Amer. Math. Soc. 139 (2011), no. 2, 675–685.