Research |
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I am interested in nonlinear
problems in differential geometry, partial differential equations,
and geometric topology. |
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Papers |
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The Morse index of a
minimal surface to appear Notices Amer. Math. Soc. (joint with O. Chodosh) |
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Waist inequality for
3-manifolds with positive scalar curvature to appear in Perspectives on Scalar Curvature, World Scientific Publishing Company (joint with Y. Liokumovich) |
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On
the topology and index of minimal surfaces II to appear in J. Differential Geom. (joint with O. Chodosh) |
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A
note on minimal surfaces with bounded index to appear in Comm. Anal. Geom. |
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Minimal
surfaces with bounded index Invent. Math. 209 (2017), no. 3, 617–664. (joint with O. Chodosh and D. Ketover) |
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Almost-rigidity
and the extinction time of positively curved Ricci flows Math. Ann. 369 (2017), no. 1-2, 899–911. (joint with R. Bamler) |
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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) |
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Free
boundary minimal annuli in convex three-manifolds J. Differential Geom. 106 (2017), no. 1, 139–186. (joint with I. Nunes and G. Smith) |
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On
the topology and index of minimal surfaces J. Differential Geom. 104 (2016), no. 3, 399–418 (joint with O. Chodosh) |
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On
the blow-up of four-dimensional Ricci flow singularities J. Reine Angew. Math. 692 (2014), 153–171. |
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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) |
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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) |
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Non-negative
Ricci curvature on closed manifolds under Ricci flow Proc. Amer. Math. Soc. 139 (2011), no. 2, 675–685. |