D-Index & Metrics Best Publications

Simon Brendle

Columbia University
United States

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name Citations Publications World Ranking National Ranking

Mathematics D-index 31 Citations 4,674 139 World Ranking 2560 National Ranking 1072

Research.com Recognitions

Awards & Achievements

2006 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study Simon Brendle is best known for:

Curvature
Riemannian manifold
Mean curvature flow

In his papers, Simon Brendle integrates diverse fields, such as Curvature and Ricci-flat manifold. Ricci-flat manifold and Scalar curvature are two areas of study in which he engages in interdisciplinary work. Simon Brendle performs integrative study on Scalar curvature and Riemannian manifold. Borrowing concepts from Curvature, he weaves in ideas under Riemannian manifold. His study ties his expertise on Dimension (graph theory) together with the subject of Pure mathematics. Many of his studies involve connections with topics such as Pure mathematics and Dimension (graph theory). His Mathematical analysis study frequently links to related topics such as Boundary (topology). Boundary (topology) and Mathematical analysis are commonly linked in his work. Many of his studies on Geometry involve topics that are commonly interrelated, such as Scaling.

His most cited work include:

Area-minimizing projective planes in 3-manifolds (35 citations)
Einstein manifolds with nonnegative isotropic curvature are locally symmetric (31 citations)
A family of curvature flows on surfaces with boundary (31 citations)

What are the main themes of his work throughout his whole career to date

Simon Brendle regularly ties together related areas like Surface (topology) in his Geometry studies. His Pure mathematics study frequently links to adjacent areas such as Conjecture. His Conjecture study frequently involves adjacent topics like Combinatorics. His Combinatorics study frequently links to related topics such as Dimension (graph theory). His research is interdisciplinary, bridging the disciplines of Pure mathematics and Dimension (graph theory). He applies his multidisciplinary studies on Curvature and Geodesic in his research. In his works, Simon Brendle performs multidisciplinary study on Geodesic and Curvature. Many of his studies on Mathematical analysis involve topics that are commonly interrelated, such as Boundary (topology). His research brings together the fields of Mathematical analysis and Boundary (topology).

Simon Brendle most often published in these fields:

Geometry (93.75%)
Pure mathematics (87.50%)
Curvature (87.50%)

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Manifolds with 1/4-pinched curvature are space forms

Simon Brendle;Richard M. Schoen.
Journal of the American Mathematical Society (2008)

430 Citations

Blow-up phenomena for the Yamabe equation

Simon Brendle.
Journal of the American Mathematical Society (2007)

273 Citations

Constant mean curvature surfaces in warped product manifolds

Simon Brendle.
Publications Mathématiques de l'IHÉS (2013)

227 Citations

Blow-up phenomena for the Yamabe equation II

Simon Brendle;Fernando C. Marques.
Journal of Differential Geometry (2009)

216 Citations

Convergence of the Yamabe flow for arbitrary initial energy

Simon Brendle.
Journal of Differential Geometry (2005)

210 Citations

Embedded minimal tori in S3 and the Lawson conjecture

Simon Brendle.
Acta Mathematica (2013)

194 Citations

Rotational symmetry of self-similar solutions to the Ricci flow

Simon Brendle.
Inventiones Mathematicae (2013)

181 Citations

Convergence of the Yamabe flow in dimension 6 and higher

Simon Brendle.
Inventiones Mathematicae (2007)

157 Citations

Classification of manifolds with weakly 1/4-pinched curvatures

Simon Brendle;Richard M. Schoen.
Acta Mathematica (2008)

137 Citations

Asymptotic behavior of flows by powers of the Gaussian curvature

Simon Brendle;Kyeongsu Choi;Panagiota Daskalopoulos.
Acta Mathematica (2017)

127 Citations

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Frequent Co-Authors

External Links

Personal Website for Simon Brendle