Christos Mantoulidis
Rice University, TX·Mathematics & Statistics
Riemannian geometry studies shapes in any number of dimensions. Besides lengths and angles, two of its central ideas are minimal surfaces, which generalize straight lines to curved spaces (a soap film is a familiar example), and curvature, which measures how a shape bends.
- Fields
Mathematics & Statistics
Physics
- Topics
minimal surfaces
minimal hypersurfaces
Riemannian geometry
- Grants
- 1 known grant, through May 2027
What they work on
- 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.
- Study enhanced rigidity properties of critical points in the van der Waals–Cahn–Hilliard theory of phase transitions in alloys, which behave like diffuse versions of minimal surfaces.
- Study the extreme behavior of quasi-local mass notions in general relativity through their interplay with scalar curvature (energy density) and minimal surfaces (black hole boundaries).
More about the research
This project studies problems about minimal surfaces and curvature that come from physics. Two sources are Einstein's general theory of relativity and the van der Waals–Cahn–Hilliard theory of phase transitions, which describes how mixed alloy materials separate into distinct regions.
Why it matters
This is pure mathematics. It aims to deepen understanding of how minimal surfaces can develop singularities and how rigid they are. It also connects that geometry to physical ideas: mass and black-hole boundaries in general relativity, and phase separation in alloy materials. These results could eventually inform the mathematical foundations of those physical theories.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
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.
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.
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.
The school
Rice University: 24 labs on PI Pages, $278M a year on research, 267 research doctorates a year.
Reach out
A start for your email. Fill in the brackets.