What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Quantum mechanics
- Partial differential equation
The scientist’s investigation covers issues in Mathematical analysis, Partial differential equation, Boundary value problem, First-order partial differential equation and Laplace operator.
He regularly links together related areas like Viscous liquid in his Mathematical analysis studies.
His Partial differential equation research integrates issues from Differential operator, Evolution equation and Existence theorem.
His biological study deals with issues like Scattering, which deal with fields such as Spectral theory.
His research in First-order partial differential equation intersects with topics in Differential algebraic equation, Parabolic partial differential equation, Elliptic partial differential equation and Method of characteristics.
Within one scientific family, he focuses on topics pertaining to Lipschitz domain under Laplace operator, and may sometimes address concerns connected to Dirichlet problem, Codimension, Differential form and Mixed boundary condition.
His most cited work include:
- Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds (782 citations)
- Partial Differential Equations I: Basic Theory (678 citations)
- Partial Differential Equations III (405 citations)
What are the main themes of his work throughout his whole career to date?
Michael Taylor spends much of his time researching Mathematical analysis, Pure mathematics, Lipschitz continuity, Nonlinear system and Mathematical physics.
Boundary value problem, Bounded function, Laplace operator, Riemannian manifold and Wave equation are among the areas of Mathematical analysis where Michael Taylor concentrates his study.
When carried out as part of a general Boundary value problem research project, his work on Mixed boundary condition is frequently linked to work in Navier–Stokes equations, therefore connecting diverse disciplines of study.
Michael Taylor studies Lipschitz continuity, focusing on Lipschitz domain in particular.
The various areas that Michael Taylor examines in his Nonlinear system study include Standing wave, Uniqueness, Classical mechanics and Schrödinger equation.
Michael Taylor works mostly in the field of Mathematical physics, limiting it down to topics relating to Eigenvalues and eigenvectors and, in certain cases, Laurent series, Computational physics, Resolvent and Constant.
He most often published in these fields:
- Mathematical analysis (48.07%)
- Pure mathematics (33.15%)
- Lipschitz continuity (14.92%)
What were the highlights of his more recent work (between 2008-2020)?
- Mathematical analysis (48.07%)
- Pure mathematics (33.15%)
- Riemannian manifold (7.73%)
In recent papers he was focusing on the following fields of study:
His primary areas of study are Mathematical analysis, Pure mathematics, Riemannian manifold, Nonlinear system and Mathematical physics.
Lipschitz domain, Lipschitz continuity, Fourier transform, Fourier analysis and Class are among the areas of Mathematical analysis where the researcher is concentrating his efforts.
His Pure mathematics study deals with Domain intersecting with Positive harmonic function, Metric tensor, Bôcher's theorem and Potential theory.
His work deals with themes such as Bounded function, Ricci decomposition, Ricci curvature, Ricci flow and Differential geometry, which intersect with Riemannian manifold.
His Nonlinear system study integrates concerns from other disciplines, such as Continuum mechanics, Classical mechanics and Standing wave.
His Mathematical physics research is multidisciplinary, incorporating perspectives in Intensity, Diffusion and Laplace operator.
Between 2008 and 2020, his most popular works were:
- Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains (95 citations)
- Hardy Spaces and bmo on Manifolds with Bounded Geometry (54 citations)
- NONLINEAR WAVES ON 3D HYPERBOLIC SPACE (33 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Quantum mechanics
- Partial differential equation
His primary areas of investigation include Mathematical analysis, Pure mathematics, Nonlinear system, Riemannian manifold and Hardy space.
His Mathematical analysis research incorporates elements of Curvature of Riemannian manifolds and Euclidean geometry.
His work on Sobolev space, Ergodic theory and Ergodic hypothesis as part of general Pure mathematics study is frequently linked to Cauchy problem, bridging the gap between disciplines.
His research integrates issues of Differential equation, Applied mathematics and Schrödinger equation in his study of Nonlinear system.
The Riemannian manifold study combines topics in areas such as Bounded function, Eigenfunction and Laplace operator.
His Hardy space research includes themes of Geometry and Differential operator.
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