Project Grant 2405361
- This National Science Foundation award provides $114,897 to the University of Texas at Dallas under the Mathematical and Physical Sciences program (CFDA 47.049) from August 1, 2022 through July 31, 2025. The principal investigator will conduct research on the existence and properties of minimal surfaces in hyperbolic 3-manifolds. Minimal surfaces are locally area-minimizing geometric objects with applications across various fields including materials science, biology, and low-dimensional...
- This $234,391 National Science Foundation project grant supports research into mean curvature flow and singular minimal surfaces at The Johns Hopkins University from August 2022 through July 2025. The grant funds mathematical research into properties of singular minimal surfaces and singular mean curvature flows, and how Colding-Minicozzi entropy relates to properties of minimal submanifolds. Researchers will also study singular minimal surfaces modeled on soap film singularities. The work...
- The National Science Foundation (NSF) awarded a $421,998 Project Grant to the University of Chicago to support research on minimal surfaces, which are important mathematical objects with applications in physics, material science, and other fields. The funding, provided under NSF's Mathematical and Physical Sciences program (CFDA 47.049), will allow the university to study the flexibility and rigidity of minimal surfaces in various geometric spaces. The project aims to deepen the understanding of...
- This federal Project Grant award, valued at $235,375, was provided by the National Science Foundation (NSF) through its Mathematical and Physical Sciences (CFDA 47.049) program. The grant supports research by the principal investigator at Rutgers, The State University, to develop new techniques for studying minimal surfaces and exploring their applications in topology and geometry. The key objectives of this 3-year project include discovering new minimal surfaces, studying the relationship...
- Federal Grant Award Summary The National Science Foundation's Division of Mathematical Sciences awarded a Project Grant of $199,999 to Princeton University effective September 1, 2025, through August 31, 2028, under the Mathematical and Physical Sciences program (CFDA 47.049). The principal investigator will conduct fundamental research investigating the variational theory of minimal surfaces and their applications across differential geometry, topology, and mathematical physics. The research...
- The National Science Foundation awarded a $250,573 Project Grant to the University of Notre Dame under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research into singular structures of minimal surfaces and higher dimensional minimal hypersurfaces. Specifically, the Principal Investigator will study the singular set geometry and behavior near singularities of minimal surfaces, as well as classify certain 8-dimensional minimal hypersurfaces in Euclidean space...
- This $380,500 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research at New York University (NYU) on scalar curvature and geometric variational problems. The project aims to advance the understanding of scalar curvature, which describes the local bending of space, and its effects on the global properties of manifolds. Key focus areas include the obstruction problem for manifolds with positive scalar curvature, geometric comparison...
- This three-year, $364,931 National Science Foundation Division of Mathematical Sciences Project Grant supports research in comparison geometry and the mentoring of students at the University of California, Riverside. The principal investigator and collaborators will investigate three fundamental problems in Riemannian geometry: the diffeomorphism stability question, the pinching problem in positive curvature, and the construction of manifolds with almost non-negative curvature. Specifically, the...
- This Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $191,477 to support research investigating hyperbolic manifolds of finite-volume through understanding the structure of their embedded submanifolds. The award to the Regents of the University of Minnesota from August 15, 2022 to July 31, 2025 will fund three main research directions: continuing work on effective virtual properties...
- This $234,951 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into nonlinear partial differential equations and minimal submanifolds in Lagrangian geometry. The project, conducted by the University of North Carolina at Chapel Hill, will generate research opportunities for graduate students and facilitate the mentoring of graduate students and postdocs. The research will focus on two key areas:...
VARIATIONAL PROBLEMS IN THE THEORY OF MINIMAL SURFACES -A SUBMANIFOLD IS CALLED MINIMAL IF IT IS A CRITICAL POINT OF THE AREA FUNCTIONAL. MINIMAL SUBMANIFOLDS ARE OF CENTRAL IMPORTANCE IN DIFFERENTIAL GEOMETRY AND ARISE NATURALLY IN MATHEMATICAL PHYSICS, AS SOAP FILMS AND BLACK HOLE HORIZONS, FOR EXAMPLE. THEREFORE, UNDERSTANDING THEIR BEHAVIOR IS OF GREAT INTEREST FROM THE MATHEMATICAL POINT OF VIEW BUT ALSO FOR APPLICATIONS. THE OBJECTIVE OF THIS PROJECT IS TO TAKE STEPS TOWARDS A FULL DESCRIPTION OF ALL MINIMAL SUBMANIFOLDS IN A GIVEN AMBIENT MANIFOLD, INSPIRED BY THE VARIATIONAL NATURE OF THESE OBJECTS. THE INVESTIGATOR WILL ALSO CONDUCT EDUCATIONAL ACTIVITIES AND PRACTICE COMMUNITY BUILDING, WITH PARTICULAR ATTENTION TO STUDENTS AND JUNIOR RESEARCHERS. THE PROJECT CONSISTS OF THREE INTERWOVEN RESEARCH LINES. THE FIRST SEEKS NEW INSIGHTS INTO THE TOPOLOGICAL AND ANALYTICAL PROPERTIES OF MINIMAL SURFACES OBTAINED VIA MIN-MAX CONSTRUCTIONS. THE SECOND LINE FOCUSES ON MINIMAL SURFACES WITH FREE BOUNDARY IN THE THREE-DIMENSIONAL BALL, WITH A FOCUS ON EXISTENCE THEOREMS AND GLOBAL PROPERTIES. FINALLY, THE PROJECT WILL INVESTIGATE RIGIDITY RESULTS FOR MINIMAL SUBMANIFOLDS OF HIGHER CODIMENSION IN AMBIENT MANIFOLDS WITH POSITIVE CURVATURE. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.- SUBAWARDS ARE NOT PLANNED FOR THIS AWARD.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $0 | 2/20/25 | ||
| Not listed | $195.0k | 5/2/24 |