Shiferaw Berhanu
University of Maryland, MD·Mathematics & Statistics
Partial differential equations describe how several quantities that depend on one another change together. They appear throughout models in science, engineering and the social sciences.
- Fields
Mathematics & Statistics
- Topics
several complex variables
CR manifolds
CR mappings
- Grants
- 1 known grant, through Jun 2028
What they work on
- Determine the geometric conditions on two embedded CR manifolds M and M' under which a CR mapping that vanishes to infinite order at a point must vanish identically near that point.
- Study unique continuation for second-order subelliptic partial differential equations with real analytic coefficients and for second-order elliptic equations with Gevrey coefficients, which are closely related to CR mappings.
- Investigate the regularity, or smoothness, of CR mappings and CR functions defined on CR manifolds.
- Explore the Radó property for continuous CR functions and the strong maximum principle for CR functions.
More about the research
This project asks a question about maps between higher-dimensional curved surfaces in the setting of several complex variables, the math of functions with more than one complex number as input. Roughly, the question is: when does tiny, infinitesimal information about such a map at one point determine how it behaves on a larger scale? This property is called unique continuation.
Why it matters
This is pure mathematics. It adds a deeper understanding of when local information about maps and solutions of partial differential equations determines their global behavior in several complex variables. Partial differential equations underpin models across the sciences and engineering, so these results could eventually inform how such equations are analyzed. A planned graduate book will make recent advances in function theory more accessible.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Jiuyi Zhu
Louisiana State University, LA·Mathematics & Statistics
Estimate the size of zero-level (nodal) sets of Laplacian eigenfunctions for second-order and higher-order elliptic equations, and determine how that size depends on high frequency.
Pablo Raúl Stinga
Iowa State University, IA·Mathematics & Statistics
Establish the analytical theory of surfaces of minimum mean curvature variation, smoothly bending surfaces used in data interpolation, image repair and hull design, including well-posedness and regularity of their equations.
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
University of Maryland: 49 labs on PI Pages, $1.5B a year on research, 602 research doctorates a year.
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