What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Pure mathematics
- Geometry
Pure mathematics, Mathematical analysis, Geodesic, Curvature and Plane curve are his primary areas of study.
Peter W. Michor regularly ties together related areas like Discrete mathematics in his Pure mathematics studies.
His Mathematical analysis study combines topics in areas such as Scalar curvature and Information geometry.
His Geodesic research is multidisciplinary, relying on both Equivalence of metrics, Metric, Fundamental theorem of Riemannian geometry, Metric space and Sobolev space.
He usually deals with Curvature and limits it to topics linked to Space and Modulo.
His work carried out in the field of Differential geometry brings together such families of science as Multivariable calculus, Global analysis, Differential form and Holomorphic function.
His most cited work include:
- The Convenient Setting of Global Analysis (919 citations)
- Natural operations in differential geometry (804 citations)
- Riemannian Geometries on Spaces of Plane Curves (345 citations)
What are the main themes of his work throughout his whole career to date?
The scientist’s investigation covers issues in Pure mathematics, Mathematical analysis, Geodesic, Diffeomorphism and Algebra.
The Pure mathematics study combines topics in areas such as Space, Group and Metric.
Peter W. Michor is involved in the study of Mathematical analysis that focuses on Differential geometry in particular.
Peter W. Michor combines subjects such as Sobolev space, Curvature, Invariant, Plane curve and Riemannian geometry with his study of Geodesic.
As a part of the same scientific study, he usually deals with the Diffeomorphism, concentrating on Combinatorics and frequently concerns with Type, Tangent vector and Homogeneous space.
His Lie group study incorporates themes from Bounded function and Lie algebra.
He most often published in these fields:
- Pure mathematics (68.79%)
- Mathematical analysis (32.62%)
- Geodesic (20.57%)
What were the highlights of his more recent work (between 2010-2020)?
- Pure mathematics (68.79%)
- Geodesic (20.57%)
- Diffeomorphism (15.60%)
In recent papers he was focusing on the following fields of study:
Peter W. Michor focuses on Pure mathematics, Geodesic, Diffeomorphism, Sobolev space and Mathematical analysis.
His primary area of study in Pure mathematics is in the field of Manifold.
His Geodesic research is multidisciplinary, incorporating perspectives in Curvature, Invariant, Plane curve, Riemannian geometry and Differential geometry.
His research on Diffeomorphism also deals with topics like
- Combinatorics which connect with Lie group, Type, Tangent vector and Vector space,
- Closed manifold that intertwine with fields like Information geometry.
He has researched Sobolev space in several fields, including Solving the geodesic equations, Order, Metric, Riemannian manifold and Submanifold.
As part of one scientific family, Peter W. Michor deals mainly with the area of Mathematical analysis, narrowing it down to issues related to the Exponential map, and often Ricci curvature.
Between 2010 and 2020, his most popular works were:
- Overview of the Geometries of Shape Spaces and Diffeomorphism Groups (123 citations)
- Sobolev metrics on shape space of surfaces (101 citations)
- Constructing reparameterization invariant metrics on spaces of plane curves (75 citations)
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