Otis Chodosh

associate professor, mathematics, Stanford

office: 380-383DD

email: ochodosh@stanford.edu

research interests: geometric analysis and PDE

graduate students:

Haotian Xue
Henry Bosch
Yujie Wu, Capillary hypersurfaces and variational methods in positively curved manifolds with boundary (2025)
Jared Marx-Kuo, Renormalizations and regularizations of minimal submanifolds, co-advised with Rafe Mazzeo (2024)
Shuli Chen, (In)stability of minimal surfaces, generalizations, and applications (2024)

papers:

Immersions with small normal curvature (with Chao Li) [arXiv:2602.15728]
Generic regularity for minimizing hypersurfaces in dimension 11 (with Christos Mantoulidis, Felix Schulze, and Zhihan Wang) [arXiv:2506.12852]
Weiss monotonicity and capillary hypersurfaces (with Nick Edelen and Chao Li) [arXiv:2506.02146]
The p-widths of a polygon (with Sithipont Cholsaipant) [arXiv:2505.03047]
3-manifolds with positive scalar curvature and bounded geometry (with Yi Lai and Kai Xu) to appear in Comm. Pure Appl. Math [arXiv:2502.09727] [journal]
Revisiting generic mean curvature flow in R^3 (with Kyeongsu Choi, Christos Mantoulidis, and Felix Schulze) to appear in J. Reine Angew. Math. (special bicentennial volume) [arXiv:2409.01463] [journal]
Complete Riemannian 4-manifolds with uniformly positive scalar curvature (with Davi Maximo and Anubhav Mukherjee) [arXiv:2407.05574]
Improved regularity for minimizing capillary hypersurfaces (with Nick Edelen and Chao Li) Ars Inven. Anal., Paper No. 2, 27 pp. (2025) [arXiv:2401.08028] [journal][MR 4888466]
On minimizers in the liquid drop model (with Ian Ruohoniemi) Comm. Pure Appl. Math., vol. 78, no. 2, 366–381 (2025). [arXiv:2401.04822] [journal] [MR 4837433]
Stable minimal hypersurfaces in R^5 (with Chao Li, Paul Minter, and Doug Stryker) to appear in Ann. of Math [arXiv:2401.01492] [journal]
Mean curvature flow from conical singularities (with Joshua Daniels-Holgate and Felix Schulze), Invent. Math., vol. 238, no. 3, 1041–1066 (2024). [arXiv:2312.00759] [journal] [MR 4824733]
Mean curvature flow with generic low-entropy initial data II (with Christos Mantoulidis and Felix Schulze), Duke Math. J., vol. 174, no. 13, pp. 2765–2819 (2025) [arXiv:2309.03856] [journal] [MR 4964789]
Improved generic regularity of codimension-1 minimizing integral currents (with Christos Mantoulidis and Felix Schulze) Ars Inven. Anal., Paper No. 3, 15 pp. (2024) [arXiv:2306.13191] [journal] [MR 4753940]
On the Minkowski inequality near the sphere (with Michael Eichmair and Thomas Körber) [arXiv:2306.03848]
Mean curvature flow with generic initial data II (with Kyeongsu Choi and Felix Schulze) [arXiv:2302.08409]
Generic regularity for minimizing hypersurfaces in dimensions 9 and 10 (with Christos Mantoulidis and Felix Schulze), to appear in Publ. Math. IHES [arXiv:2302.02253]
Volume growth of 3-manifolds with scalar curvature lower bounds (with Chao Li and Doug Stryker), Proc. Amer. Math. Soc., 151, no. 10, 4501–4511 (2023). [arXiv:2207.13806] [journal] [MR 4643334]
Stable anisotropic minimal hypersurfaces in R^4 (with Chao Li), Forum of Math. Pi, 11, e3 (2023). [arXiv:2206.06394] [journal] [MR 4546104]
Complete stable minimal hypersurfaces in positively curved 4-manifolds (with Chao Li and Doug Stryker), J. Eur. Math. Soc. 28, no. 4, pp. 1457–1487 (2026). [arXiv:2202.07708] [journal] [MR 5032982]
Stable minimal hypersurfaces in R^4 (with Chao Li), Acta Math., vol. 233, 1–31 (2024) [arXiv:2108.11462] [journal] [MR 4816633] [errata]
The p-widths of a surface (with Christos Mantoulidis), Publ. Math. IHES, vol. 137, 245–342 (2023) [arXiv:2107.11684] [journal] [MR 4588597]
Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions (with Chao Li and Yevgeny Liokumovich), Geom. Topol., no. 27, 1635–1655 (2023) [arXiv:2105.07306] [journal] [MR 4602422]
Mean curvature flow with generic low-entropy initial data (with Kyeongsu Choi, Christos Mantoulidis, and Felix Schulze), Duke Math. J., vol. 173, no. 7, pp. 1269–1290 (2024) [arXiv:2102.11978] [journal] [MR4757533]
Generalized soap bubbles and the topology of manifolds with positive scalar curvature (with Chao Li), Ann. of Math. vol. 199, no. 2, pp. 707–740 (2024) [arXiv:2008.11888] [journal] [MR 4713021]
Singular behavior and generic regularity of min-max minimal hypersurfaces (with Yevgeny Liokumovich and Luca Spolaor), Ars Inven. Anal., Paper No. 2, 27 pp. (2022). [arXiv:2007.11560] [journal] [MR 4462477]
Mean curvature flow with generic initial data (with Kyeongsu Choi, Christos Mantoulidis, and Felix Schulze), Invent. Math., vol. 237, no. 1, pp. 121–220 (2024) [arXiv:2003.14344] [journal] [MR4756990]
The Riemannian quantitative isoperimetric inequality (with Max Engelstein and Luca Spolaor), J. Eur. Math. Soc., vol. 25, no. 5, 1711–1741 (2023) [arXiv:1908.00677] [journal] [MR 4592858]
Uniqueness of asymptotically conical tangent flows (with Felix Schulze), Duke Math. J., vol. 170, no. 16, pp. 3601–3657 (2021). [arXiv:1901.06369] [journal] [MR 4332673]
Minimal hypersurfaces with arbitrarily large area (with Christos Mantoulidis), Int. Math. Res. Not., no. 14, 10841–10847 (2021). [arXiv:1901.05893] [journal] [MR 4285736]
On the topology and index of minimal surfaces II (with Davi Maximo), J. Differential Geom., vol. 123, no. 3, pp. 431–459 (2023). [arXiv:1808.06572] [journal] [MR 4584858]
A splitting theorem for scalar curvature (with Michael Eichmair and Vlad Moraru), Comm. Pure Appl. Math., vol. 72, no. 6, pp. 1231–1242 (2019). [arXiv:1804.01751] [journal] [MR 3948556]
Characterization of large isoperimetric regions in asymptotically hyperbolic initial data (with Michael Eichmair, Yuguang Shi, and Jintian Zhu), Comm. Math. Phys., vol. 368, no. 2, pp. 777–798 (2019). [arXiv:1804.00447] [journal] [MR3949724]
Minimal surfaces and the Allen–Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates (with Christos Mantoulidis), Ann. of Math., vol. 191, no. 1, pp. 213–328 (2020). [arXiv:1803.02716] [journal] [MR 4045964]
Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces (with Costante Bellettini and Neshan Wickramasekera), Adv. Math., vol. 352, pp. 133–157 (2019). [arXiv:1802.08928] [journal] [MR 3959653]
Asymptotically flat three-manifolds contain minimal planes (with Daniel Ketover), Adv. Math., vol. 337, pp. 171–192 (2018). [arXiv:1709.09650] [journal] [MR 3853048]
On far-outlying CMC spheres in asymptotically flat Riemannian 3-manifolds (with Michael Eichmair), J. Reine Angew. Math., vol. 767, pp. 161–191 (2020). [arXiv:1703.09557] [journal] [MR 4160305]
Global uniqueness of large stable CMC spheres in asymptotically flat Riemannian three-manifolds (with Michael Eichmair), Duke Math. J., vol. 171, no. 1, pp. 1–31 (2022). [arXiv:1703.02494] [journal] [MR 4364730]
Isoperimetry, scalar curvature, and mass in asymptotically flat Riemannian 3-manifolds (with Michael Eichmair, Yuguang Shi, and Haobin Yu), Comm. Pure Appl. Math., vol. 74, no.4, pp. 865--905 (2021). [arXiv:1606.04626] [journal] [Oberwolfach report] [MR 4221936]
Time-periodic Einstein–Klein–Gordon bifurcations of Kerr (with Yakov Shlapentokh-Rothman), Comm. Math. Phys., vol. 356, no. 3, pp. 1155–1250 (2017). [arXiv:1510.08025] [journal] [MR 3719550]
Stationary axisymmetric black holes with matter (with Yakov Shlapentokh-Rothman), Comm. Anal. Geom., vol. 29, no. 1, pp. 19–76 (2021). [arXiv:1510.08024] [journal] [MR 4234978]
Area-minimizing surfaces in asymptotically flat three-manifolds (with Michael Eichmair). Included with this paper for publication. [arXiv:1510.07406]
Minimal hypersurfaces with bounded index (with Daniel Ketover and Davi Maximo), Invent. Math., vol. 209, no. 3, pp. 617–664 (2017). [arXiv:1509.06724] [journal] [MR 3681392]
Effective versions of the positive mass theorem (with Alessandro Carlotto and Michael Eichmair), Invent. Math., vol. 206, no. 3, pp. 975–1016 (2016). [arXiv:1503.05910] [journal] [MR 3573977]
On the maximum curvature of closed curves in negatively curved manifolds (with Simon Brendle), Canad. Math. Bull., vol. 58, no. 4, pp. 713–722 (2015). [local version] [journal] [MR 3415662]
On the topology and index of minimal surfaces (with Davi Maximo), J. Differential Geom., vol. 104, no. 3, pp. 399–418 (2016). [arXiv:1405.7356] [journal] [MR 3568626] [Oberwolfach report]
Isoperimetric structure of asymptotically conical manifolds (with Michael Eichmair and Alexander Volkmann), J. Differential Geom., vol. 105, no. 1, pp. 1–19 (2017). [arXiv:1503.05181] [journal] [MR 3592692]
Large isoperimetric regions in asymptotically hyperbolic manifolds, Comm. Math. Phys., vol. 343, no. 2, pp. 393–443 (2016). [arXiv:1403.6108] [journal] [MR 3477343]
Slowly converging Yamabe flows (with Alessandro Carlotto and Yanir Rubinstein), Geom. Topol., vol. 19, no. 3, pp. 1523–1568 (2015). [arXiv:1401.3738] [journal] [MR 3352243] [errata]
On discontinuity of planar optimal transport maps (with Vishesh Jain, Michael Lindsey, Lyuboslav Panchev and Yanir Rubinstein), J. Topol. Anal., vol. 7, no. 2, pp. 239–260 (2015). This research was carried out by our group mainly during a 2012 SURIM REU. [arXiv:1312.2929] [journal] [MR 3326301]
A volume comparison theorem for asymptotically hyperbolic manifolds (with Simon Brendle), Comm. Math. Phys., vol. 332, no. 2, pp. 839–846 (2014). [arXiv:1305.6628] [journal] [MR 3257665]
Rotational symmetry of conical Kähler-Ricci solitons (with Frederick Tsz-Ho Fong), Math. Ann., vol. 364, no. 3, pp. 777–792 (2016). [arXiv:1304.0277] [journal] [MR 3466851]
Expanding Ricci solitons asymptotic to cones, Calc. Var. Partial Differential Equations, vol. 51, no. 1-2, pp. 1–15 (2014). [arXiv:1303.2983] [journal] [MR 3247379]
A lack of Ricci bounds for the entropic measure on Wasserstein space over the interval, J. Funct. Anal., vol. 262, no. 10, pp. 4570–4581 (2012). A condensed version of my Part III essay. [arXiv:1111.0058] [journal] [MR 2900478]
Infinite matrix representations of isotropic pseudodifferential operators, Methods Appl. Anal., vol. 18, no. 4, pp. 351–372 (2011). A condensed (and expanded) version of my undergraduate thesis. [arXiv:1101.4459] [journal] [MR 2965982]

theses:

The geometry of asymptotically hyperbolic manifolds. Ph.D. thesis (advised by Simon Brendle and co-advised by Michael Eichmair).
Optimal transport and Ricci curvature: Wasserstein space over the interval. Part III essay (supervised by Clément Mouhot). [arXiv:1105.2883]
Infinite matrix representations of classes of pseudodifferential operators. Undergraduate thesis (supervised by András Vasy).