2026 Peter B. Gilkey: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	38	2272	2012	960	799	346	12413

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

2272

2012

960

799

346

12413

Research.com Recognitions

2013 - Fellow of the American Mathematical Society
1975 - Fellow of Alfred P. Sloan Foundation

Overview

Peter B. Gilkey is affiliated with the University of Oregon in the United States. Their research work spans various areas within mathematics, with a primary focus on geometric analysis, topology, and mathematical physics.

The main fields of study for Gilkey include:

Mathematics

Within these fields, their contributions are concentrated in several subfields such as:

Applied Mathematics
Geometry and Topology
Mathematical Physics
Computational Theory and Mathematics
Astronomy and Astrophysics

The topics central to their research activity include:

Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Geometric and Algebraic Topology
Advanced Mathematical Modeling in Engineering
Advanced Operator Algebra Research
Numerical methods in inverse problems
Spectral Theory in Mathematical Physics

Recent publications by Peter B. Gilkey demonstrate engagement with harmonic analysis and geometric structures:

"Harmonic Spaces and Density Functions", 2020, Results in Mathematics
"Maximal Domains of Radial Harmonic Functions", 2023, Mediterranean Journal of Mathematics
"Harmonic radial vector fields on harmonic spaces", 2021, Journal of Mathematical Analysis and Applications

Other notable papers listed include:

"The local index density of the perturbed de Rham complex", 2021, Czechoslovak Mathematical Journal
"On distinguished local coordinates for locally homogeneous affine surfaces", 2020, Monatshefte für Mathematik

Peter B. Gilkey has frequently collaborated with several researchers, including:

JeongHyeong Park
Eduardo García-Río
Esteban Calviño-Louzao
Ramón Vázquez-Lorenzo
Jesús A. Álvarez López

The venues in which Gilkey most often publishes are:

arXiv (Cornell University)
Czechoslovak Mathematical Journal
Monatshefte für Mathematik
Mediterranean Journal of Mathematics
Results in Mathematics

Gilkey has also contributed to academia through book publications, notably:

Aspects of Differential Geometry V (2021), part of the Synthesis Lectures on Mathematics and Statistics

Their career has been recognized with distinctions such as:

Fellow of the American Mathematical Society (2013)
Fellow of Alfred P. Sloan Foundation (1975)

Best Publications

Invariance theory, the heat equation, and the Atiyah-Singer index theorem

Peter B. Gilkey

2725
Citations
Gravitation, Gauge Theories and Differential Geometry

Tohru Eguchi;Tohru Eguchi;Peter B. Gilkey;Peter B. Gilkey;Andrew J. Hanson

2499
Citations
The spectral geometry of a Riemannian manifold

Peter B. Gilkey

959
Citations
The asymptotics of the Laplacian on a manifold with boundary

Thomas P. Branson;Peter B. Gilkey

426
Citations
Asymptotic Formulae in Spectral Geometry

Peter B. Gilkey

278
Citations
The index theorem and the heat equation

Peter B. Gilkey

270
Citations
Curvature and the eigenvalues of the Laplacian for elliptic complexes

Peter B Gilkey

191
Citations
Heat Content Asymptotics of a Riemannian Manifold with Boundary

M. Vandenberg;P.B. Gilkey

148
Citations
Recursion relations and the asymptotic behavior of the eigenvalues of the laplacian

Peter B. Gilkey

139
Citations
The boundary integrand in the formula for the signature and Euler characteristic of a Riemannian manifold with boundary

Peter B Gilkey

135
Citations
ISOPARAMETRIC GEODESIC SPHERES AND A CONJECTURE OF OSSERMAN CONCERNING THE JACOBI OPERATOR

Peter Gilkey;Andrew Swann;Lieven Vanhecke

133
Citations
The Geometry of Walker Manifolds

Miguel Brozos-Vázquez;Eduardo García-Río;Peter Gilkey;Stana Nikčević

127
Citations
The eta invariant and metrics of positive scalar curvature

Boris Botvinnik;Peter B. Gilkey

123
Citations
A Note on Osserman Lorentzian Manifolds

Novica Blažić;Neda Bokan;Peter Gilkey

118
Citations
Residues of the eta function for an operator of Dirac type

Thomas P. Branson;Peter B. Gilkey

103
Citations
The eta invariant for a class of elliptic boundary value problems

Peter B. Gilkey;Lance Smith

103
Citations
Heat kernel asymptotics with mixed boundary conditions

Thomas P. Branson;Peter B. Gilkey;Klaus Kirsten;Dmitri V. Vassilevich

100
Citations
Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor

Peter B Gilkey

98
Citations
The residue of the global η function at the origin

Peter B. Gilkey

96
Citations
On the Index of Geometrical Operators for Riemannian-Manifolds with Boundary

P.B. Gilkey

92
Citations

Frequent Co-Authors

Klaus Kirsten Baylor University

Thomas P. Branson University of Iowa

Dmitri Vassilevich Universidade Federal do ABC

Joseph A. Wolf University of California, Berkeley

Alexander Grigor'yan Bielefeld University

Gary M. Seitz University of Oregon

Lieven Vanhecke KU Leuven

External Links

Wikipedia of Peter B. Gilkey Personal website of Peter B. Gilkey

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