Otis Chodosh
Stanford University, CA·Mathematics & Statistics
Many shapes in nature settle into the configuration that uses the least energy. A soap film stretched across a wire loop, for example, takes the shape with the smallest possible surface area.
- Fields
Mathematics & Statistics
- Topics
calculus of variations
minimal surfaces
minimal hypersurfaces
- Grants
- 1 known grant, through Aug 2027
What they work on
- Study questions connected to stable minimal hypersurfaces, building on the four-dimensional proof that such surfaces are flat, with the goal of resolving the stable Bernstein problem in higher dimensions.
- Investigate how stability of minimal hypersurfaces relates to scalar curvature comparison geometry, which compares how curved a space is with model spaces.
- Study stability-related problems for the Allen-Cahn equation, which models the boundary between two phases of a material.
- Investigate finite Morse index (weaker stability) in min-max constructions of minimal surfaces, and compute the area spectrum (p-widths) of surfaces beyond the two-sphere.
More about the research
The mathematics of such optimal shapes, the calculus of variations, still has many open basic questions: what do optimal configurations look like, and how much more energy does a nearby, slightly worse shape need? This project focuses on 'stability', meaning how an optimal shape compares with nearby, less optimal ones, and what stability reveals about the structure of the optimal shapes.
Why it matters
This is pure mathematics. It deepens understanding of the shape and stability of energy-minimizing configurations, such as soap films and the interfaces between phases of matter. These questions underlie models in geometry and materials science, and the results could eventually inform how such energy-minimizing models are analyzed.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Xin Zhou
Cornell University, NY·Mathematics & Statistics
Prove the existence of closed minimal surfaces with controlled genus, or number of holes, in three-manifolds, with the goal of resolving Yau's Four Minimal Spheres Conjecture.
William Minicozzi
Massachusetts Institute of Technology, MA·Mathematics & Statistics
Establish gradient estimates and monotonicity formulas for harmonic functions and heat equation solutions, clarifying how they depend on dimension and how elliptic and parabolic behavior relate.
Jonathan Zhu
University of Washington, WA·Mathematics & Statistics·Early-career
Analyze singularities of mean curvature flow near cylindrical and conical models, testing uniqueness of blow-up limits when curvature is present in the interior or at the boundary.
The school
Stanford University: 87 labs on PI Pages, $1.6B a year on research, 739 research doctorates a year.
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