What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Topology
Simon Brendle mainly focuses on Pure mathematics, Mathematical analysis, Scalar curvature, Sectional curvature and Ricci curvature.
His research on Pure mathematics focuses in particular on Conjecture.
His work investigates the relationship between Mathematical analysis and topics such as Yamabe flow that intersect with problems in Prescribed scalar curvature problem and Dimension.
He interconnects Riemannian manifold, General relativity and Conformal map in the investigation of issues within Scalar curvature.
His Sectional curvature research incorporates elements of Manifold and Ricci-flat manifold.
In his study, which falls under the umbrella issue of Ricci curvature, Riemannian geometry is strongly linked to Curvature of Riemannian manifolds.
His most cited work include:
- Manifolds with 1/4-pinched curvature are space forms (272 citations)
- Blow-up phenomena for the Yamabe equation (174 citations)
- Constant mean curvature surfaces in warped product manifolds (146 citations)
What are the main themes of his work throughout his whole career to date?
The scientist’s investigation covers issues in Mathematical analysis, Pure mathematics, Ricci flow, Curvature and Scalar curvature.
His work carried out in the field of Mathematical analysis brings together such families of science as Flow, Yamabe flow, Sectional curvature, Constant and Mean curvature flow.
The Conjecture, Dimension and Euclidean space research Simon Brendle does as part of his general Pure mathematics study is frequently linked to other disciplines of science, such as Sobolev inequality, therefore creating a link between diverse domains of science.
When carried out as part of a general Ricci flow research project, his work on Sphere theorem is frequently linked to work in Soliton, therefore connecting diverse disciplines of study.
His research on Curvature also deals with topics like
- Riemannian manifold, which have a strong connection to Boundary,
- Mathematical physics that connect with fields like Rotational symmetry.
Simon Brendle focuses mostly in the field of Scalar curvature, narrowing it down to matters related to Ricci curvature and, in some cases, Riemann curvature tensor, Curvature of Riemannian manifolds and Ricci-flat manifold.
He most often published in these fields:
- Mathematical analysis (47.89%)
- Pure mathematics (39.44%)
- Ricci flow (27.46%)
What were the highlights of his more recent work (between 2017-2021)?
- Pure mathematics (39.44%)
- Ricci flow (27.46%)
- Dimension (11.27%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Pure mathematics, Ricci flow, Dimension, Sobolev inequality and Inequality.
His research in Pure mathematics intersects with topics in Curvature and Sectional curvature.
The Curvature study which covers Manifold that intersects with Ricci curvature, Diffeomorphism and Riemann curvature tensor.
His research investigates the connection with Sectional curvature and areas like Convex function which intersect with concerns in Mean curvature flow.
His Ricci flow study combines topics from a wide range of disciplines, such as Hypersurface and Uniqueness.
His study on Inequality also encompasses disciplines like
- Euclidean space which connect with Mean curvature,
- Isoperimetric inequality together with Special case.
Between 2017 and 2021, his most popular works were:
- Ricci flow with surgery on manifolds with positive isotropic curvature (20 citations)
- Ancient solutions to the Ricci flow in dimension 3 (19 citations)
- Mean curvature flow with surgery of mean convex surfaces in three-manifolds (11 citations)
In his most recent research, the most cited papers focused on:
- Mathematical analysis
- Geometry
- Topology
His primary areas of study are Ricci flow, Pure mathematics, Dimension, Mean curvature flow and Regular polygon.
His Ricci flow research entails a greater understanding of Curvature.
He combines subjects such as Hypersurface, Manifold, Connected sum and Diffeomorphism with his study of Curvature.
His studies in Dimension integrate themes in fields like Differential and Space.
The Mean curvature flow study combines topics in areas such as Gravitational singularity, Mathematical analysis, Uniqueness, Sectional curvature and Convex function.
Soliton is connected with Work, Quotient and Singularity in his study.
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