Jonathan Zhu
University of Washington, WA·Mathematics & Statistics·Early-career
Soap films, black hole horizons and liquid surfaces in narrow tubes all take shapes governed by mean curvature, a measure of how much a surface bends on average. Minimal surfaces, which locally minimize area like soap films, and mean curvature flow, a process in which a surface moves to shrink its area, are central topics in geometric analysis.
- Fields
Mathematics & Statistics
- Topics
minimal surfaces
mean curvature flow
geometric analysis
- Grants
- 1 known grant, through Jul 2030
What they work on
- 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.
- Use min-max constructions to produce hypersurfaces with prescribed mean curvature and prescribed boundary contact angle, modeling capillary-type surfaces.
- Determine the regularity and long-time behavior of mean curvature flow with capillary boundary action, where the moving surface meets a boundary at a set angle.
- Study the complexity of submanifolds, measured by area and entropy, and its connections to the stability of minimal submanifolds.
More about the research
They connect mathematics to physics and materials science. A growing question is how these surfaces behave at a boundary, including capillary action, where a surface meets a wall at a fixed contact angle.
Why it matters
This is basic mathematics. It deepens understanding of how curvature-driven surfaces form, evolve and break down, especially at boundaries. Such surfaces model soap films, capillary interfaces and black hole horizons, so the theory could eventually inform the mathematical description of interfaces in physics and materials science.
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.
Otis Chodosh
Stanford University, CA·Mathematics & Statistics
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.
Christos Mantoulidis
Rice University, TX·Mathematics & Statistics
Investigate the structure of singularities, points where curvature blows up, in area-minimizing minimal surfaces and in mean curvature flow, where a surface evolves to reduce its area.
The school
University of Washington: 81 labs on PI Pages, $1.7B a year on research, 694 research doctorates a year.
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