The Nash embedding theorems, named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance, bending but neither stretching nor tearing a page of paper gives an isometric embedding of the page into Euclidean space because curves drawn on the page retain the same arclength however the page is bent.
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450. It is awarded every three years for a notable research work in analysis that has appeared during the past six years. The work must be published in a recognized, peer-reviewed venue. The current award is $5,000.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Luis Ángel Caffarelli is an Argentine-American mathematician. He studies partial differential equations and their applications.
Lawrence Craig Evans is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are used to establish new results in differential geometry and differential topology. The use of linear elliptic PDEs dates at least as far back as Hodge theory. More recently, it refers largely to the use of nonlinear partial differential equations to study geometric and topological properties of spaces, such as submanifolds of Euclidean space, Riemannian manifolds, and symplectic manifolds. This approach dates back to the work by Tibor Radó and Jesse Douglas on minimal surfaces, John Forbes Nash Jr. on isometric embeddings of Riemannian manifolds into Euclidean space, work by Louis Nirenberg on the Minkowski problem and the Weyl problem, and work by Aleksandr Danilovich Aleksandrov and Aleksei Pogorelov on convex hypersurfaces. In the 1980s fundamental contributions by Karen Uhlenbeck, Clifford Taubes, Shing-Tung Yau, Richard Schoen, and Richard Hamilton launched a particularly exciting and productive era of geometric analysis that continues to this day. A celebrated achievement was the solution to the Poincaré conjecture by Grigori Perelman, completing a program initiated and largely carried out by Richard Hamilton.
In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.
In mathematics, geometric measure theory (GMT) is the study of geometric properties of sets through measure theory. It allows mathematicians to extend tools from differential geometry to a much larger class of surfaces that are not necessarily smooth.
Jerry Lawrence Kazdan is an American mathematician noted for his work in differential geometry and the study of partial differential equations. His contributions include the Berger–Kazdan comparison theorem, which was a key step in the proof of the Blaschke conjecture and the classification of Wiedersehen manifolds. His best-known work, done in collaboration with Frank Warner, dealt with the problem of prescribing the scalar curvature of a Riemannian metric.
Robert "Bob" Osserman was an American mathematician who worked in geometry. He is specially remembered for his work on the theory of minimal surfaces.
Leon Melvyn Simon, born in 1945, is a Leroy P. Steele Prize and Bôcher Prize-winning mathematician, known for deep contributions to the fields of geometric analysis, geometric measure theory, and partial differential equations. He is currently Professor Emeritus in the Mathematics Department at Stanford University.
Nicola Fusco is an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equations, and the theory of symmetrization. He is currently professor at the Università di Napoli "Federico II". Fusco also taught and conducted research at the Australian National University at Canberra, the Carnegie Mellon University at Pittsburgh and at the University of Florence.
Giuseppe Mingione is an Italian mathematician who is active in the fields of partial differential equations and calculus of variations.
Jürgen Jost is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.
J. (Jean) François Treves is an American mathematician, specializing in partial differential equations.
Michael Struwe is a German mathematician who specializes in calculus of variations and nonlinear partial differential equations. He won the 2012 Cantor medal from the Deutsche Mathematiker-Vereinigung for "outstanding achievements in the field of geometric analysis, calculus of variations and nonlinear partial differential equations".
Paolo Marcellini is an Italian mathematician who deals with mathematical analysis. He was a full professor at the University of Florence, actually Professor Emeritus, who works on partial differential equations, calculus of variations and related mathematics. He was the Director of the Italian National Group GNAMPA of the Istituto Nazionale di Alta Matematica (INdAM) and Dean of the Faculty of Mathematical, Physical and Natural Sciences of the University of Florence.
Hajer Bahouri is a Franco-Tunisian mathematician who is interested in partial differential equations. She is Director of Research at the National Center for Scientific Research and the Laboratory of Analysis and Applied Mathematics at the University Paris-Est-Créteil-Val-de-Marne.
Anthony Joseph Tromba is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.
Joel Spruck is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971.
