Improved regularity for minimizing capillary hypersurfaces, joint with Otis Chodosh and Nick Edelen. arXiv

Stable minimal hypersurfaces in R^5, joint with Otis Chodosh, Douglas Stryker and Paul Minter, submitted. arXiv

Attaching faces of positive scalar curvature manifolds with corners, joint with Alessandro Carlotto, to appear in SIGMA: Symmetry, Integrability and Geometry: Method and Applications, special issue in honors of Jean-Pierre Bourguignon on the occasion of his 75th birthday. arXiv

A note about isotopy and concordance of positive scalar curvature metrics on compact manifolds with boundary, joint with Alessandro Carlotto, to appear in Beijing Journal of Pure and Applied Mathematics (the Bartnik memorial volume). arXiv

Volume growth of 3-manifolds with scalar curvature lower bounds, joint with Otis Chodosh and Douglas Stryker, Proc. Amer. Math Soc. 151 (2023), 4501-4511. arXiv

Decomposing 4-manifolds with positive scalar curvature, joint with Richard Bamler and Christos Mantoulidis, Adv. Math. , Volume 430, 2023. arXiv

Stable anisotropic minimal hypersurfaces in 𝗥⁴, joint with Otis Chodosh, Forum of Mathematics, Pi, 11, E3. arXiv

Complete stable minimal hypersurfaces in positively curved 4-manifolds, joint with Otis Chodosh and Douglas Stryker, to appear in J. Eur. Math. Soc. arXiv

Min-max theory for capillary surfaces, joint with Xin Zhou and Jonathan Zhu, to appear in J. Reine Angew. Math. arXiv

Stable minimal hypersurfaces in 𝗥⁴, joint with Otis Chodosh, Acta Math. , volume 233 (2024), no. 1, 1-31. arXiv

Constrained deformations of positive scalar curvature metrics, II, joint with Alessandro Carlotto, Comm. Pure Appl. Math. , 77 (2024): 795 - 862. arXiv

Metrics with λ₁(-Δ+kR)≥0 and flexibility in the Riemannian Penrose Inequality, joint with Christos Mantoulidis, Comm. Math. Phys. , 401 (2023), no. 2, 1831-1877. arXiv

Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions, joint with Otis Chodosh and Yevgeny Liokumovich, Geom. Topo. , 27:4 (2023), 1635-1655. arXiv

Generalized soap bubbles and the topology of manifolds with positive scalar curvature, joint with Otis Chodosh, Ann. Math. , 199 (2024), 707-740. arXiv

Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces, SIGMA 16 (2020), 099. Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday. arXiv

Regularity of free boundary minimal surfaces in locally polyhedral domains, joint with Nick Edelen, Comm. Pure Appl. Math., 75: 970-1031 (2022). arXiv

The dihedral rigidity conjecture for n-prisms , J. Differential Geom., 126(1): 329-361. arXiv

Constrained deformations of positive scalar curvature metrics , joint with A. Carlotto, J. Differential Geom., 126(2), 475-554. arXiv

Singularity and comparison theorems for metrics with positive scalar curvature , Ph.D. Thesis, Stanford University. PDF file. Video of a talk at the Institute for Advanced Study.

A polyhedron comparison theorem for three-manifolds with positive scalar curvature, Invent. Math. 219, 1-37 (2020) arXiv

Positive scalar curvature and skeleton singularities, joint with C. Mantoulidis, Math. Ann. (2019) 374: 99. arXiv

Index and topology of minimal hypersurfaces in 𝗥ⁿ, Calc. Var. (2017) 56:180. arXiv