Andrew Raich
Affiliation confirmed via AI analysis of OpenAlex, ORCID, and web sources.
Professor
Also affiliated: University of Wollongong (2016); Texas A&M University (2006–2015)
Research Areas
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Biography and Research Information
OverviewAI-generated summary
Andrew Raich's research focuses on areas of mathematical analysis, particularly concerning differential geometry and operator theory. His work has explored the properties of complex Green operators on CR-manifolds, investigating their compactness and regularity. Raich has also studied heat equations in various mathematical spaces, including R×C and quadric manifolds, and examined the behavior of the □ b -Heat Equation. His publications include investigations into closed range properties for ∂ ¯ and ∂ ¯ b on bounded hypersurfaces in Stein manifolds, as well as one-parameter families of operators in ℂ.
With a h-index of 12 and 444 citations across 92 publications, Raich has a significant body of work in his field. He has collaborated with Phillip S. Harrington, with whom he shares six publications, indicating an established academic network at the University of Arkansas at Fayetteville. His most recent publication is from 2026, demonstrating continued activity in research.
Metrics
- h-index: 13
- Publications: 90
- Citations: 476
Positions
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Professor 2018–presentUniversity of Arkansas Department of Mathematical Sciences ORCID
Selected Publications
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Global regularity for the $$\bar{\partial }$$-Neumann problem on pseudoconvex manifolds (2026)
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The ∂-problem on Z(q)-domains (2026)
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The ∂-problem on Z(q)-domains (2026)
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Geometry and Analysis of the Grusin Operator (2025)
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Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type (2025)
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Distributions with Decay and Restriction Problems (2024)
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Hardy Spaces and Canonical Kernels on Quadric CR Manifolds (2024)
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Maximal Estimates for the $${\bar{\partial }}$$-Neumann Problem on Non-pseudoconvex Domains (2024)
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The fundamental solution to □b on quadric manifolds with nonzero eigenvalues and null variables (2023)
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Global Gevrey vectors (2023)
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The fundamental solution to \Box_{𝑏} on quadric manifolds with nonzero eigenvalues (2023)
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None (2023)
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Analysis on quadrics (2022)
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Boundary invariants and the closed range property for ∂¯ (2022)
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The fundamental solution to \Box_{𝑏} on quadric manifolds – Part 1. General formulas (2022)
Collaboration Network
Top Collaborators
- The □ b -Heat Equation on Quadric Manifolds
- A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group
- Heat Kernels, Smoothness Estimates, and Exponential Decay
- Fundamental Solutions to □ b on Certain Quadrics
- The fundamental solution to $$\Box _b$$ on quadric manifolds: part 2. $$L^p$$ regularity and invariant normal forms
Showing 5 of 12 shared publications
- Regularity Results for [image omitted] on CR-Manifolds of Hypersurface Type
- Closed range of ∂¯ in L2-Sobolev spaces on unbounded domains in Cn
- Regularity equivalence of the Szegö projection and the complex Green operator
- A remark on boundary estimates on unbounded Z(q) domains in
- Closed range of $$\overline \partial $$ on unbounded domains in ℂn
Showing 5 of 11 shared publications
- Lp estimates for the $\bar\partial$-equation on a class of infinite type domains
- The Kohn-Laplace equation on abstract CR manifolds: Global regularity
- Lp‐Estimates for the ∂¯b‐equation on a class of infinite type domains
- Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type
- Global regularity for the $$\bar{\partial }$$-Neumann problem on pseudoconvex manifolds
- Global $$L^q$$-Gevrey Functions and Their Applications
- Microglobal regularity and the global wavefront set
- Distributions with Decay and Restriction Problems
- Global Gevrey vectors
- Geometry and Analysis of the Grusin Operator
- Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
- Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior
- Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
- On Div-Curl for Higher Order
- Taylor series of conformal mappings onto symmetric quadrilaterals
- THE SZEGO KERNEL ON A CLASS OF NONCOMPACT CR MANIFOLDS OF HIGH CODIMENSION
- Schrödinger Operators with A ∞ $A_{\infty }$ Potentials
- Compactness of the complex Green operator on non-pseudoconvex CR manifolds
- Closed Range Estimates for $$\bar{\partial }_b$$ on CR Manifolds of Hypersurface Type
- None
- Hardy Spaces and Canonical Kernels on Quadric CR Manifolds
- The ∂-problem on Z(q)-domains
- The ∂-problem on Z(q)-domains
- Regularity equivalence of the Szegö projection and the complex Green operator
- Lp estimates for the $\bar\partial$-equation on a class of infinite type domains
- An Aronsson type approach to extremal quasiconformal mappings
- Taylor series of conformal mappings onto symmetric quadrilaterals
- Global $$L^q$$-Gevrey Functions and Their Applications
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