In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.
In mathematics, the uniformization theorem says that every simply connected Riemann surface is conformally equivalent to one of three Riemann surfaces: the open unit disk, the complex plane, or the Riemann sphere. The theorem is a generalization of the Riemann mapping theorem from simply connected open subsets of the plane to arbitrary simply connected Riemann surfaces.
Richard Melvin Schoen is an American mathematician known for his work in differential geometry and geometric analysis. He is best known for the resolution of the Yamabe problem in 1984.
In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is a subgroup of Sp(n)·Sp(1) for some . Here Sp(n) is the sub-group of consisting of those orthogonal transformations that arise by left-multiplication by some quaternionic matrix, while the group of unit-length quaternions instead acts on quaternionic -space by right scalar multiplication. The Lie group generated by combining these actions is then abstractly isomorphic to .
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 differential geometry, the Willmore conjecture is a lower bound on the Willmore energy of a torus. It is named after the English mathematician Tom Willmore, who conjectured it in 1965. A proof by Fernando Codá Marques and André Neves was announced in 2012 and published in 2014.
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.
In differential geometry, constant-mean-curvature (CMC) surfaces are surfaces with constant mean curvature. This includes minimal surfaces as a subset, but typically they are treated as special case.
Gerhard Huisken is a German mathematician whose research concerns differential geometry and partial differential equations. He is known for foundational contributions to the theory of the mean curvature flow, including Huisken's monotonicity formula, which is named after him. With Tom Ilmanen, he proved a version of the Riemannian Penrose inequality, which is a special case of the more general Penrose conjecture in general relativity.
Henry Christian Wente was an American mathematician, known for his 1986 discovery of the Wente torus, an immersed constant-mean-curvature surface whose existence disproved a conjecture of Heinz Hopf.
Manfredo Perdigão do Carmo was a Brazilian mathematician. He spent most of his career at IMPA and is seen as the doyen of differential geometry in Brazil.
Ravindra Shripad Kulkarni is an Indian mathematician, specializing in differential geometry. He is known for the Kulkarni–Nomizu product.
Anthony Joseph Tromba is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.
William Hamilton Meeks III is an American mathematician, specializing in differential geometry and minimal surfaces.
Thomas Schick is a German mathematician, specializing in algebraic topology and differential geometry.
Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary is a book on the physical models of concepts in mathematics that were constructed in the 19th century and early 20th century and kept as instructional aids at universities. It credits Gerd Fischer as editor, but its photographs of models are also by Fischer. It was originally published by Vieweg+Teubner Verlag for their bicentennial in 1986, both in German and (separately) in English translation, in each case as a two-volume set with one volume of photographs and a second volume of mathematical commentary. Springer Spektrum reprinted it in a second edition in 2017, as a single dual-language volume.
In the mathematical field of differential geometry, a maximal surface is a certain kind of submanifold of a Lorentzian manifold. Precisely, given a Lorentzian manifold (M, g), a maximal surface is a spacelike submanifold of M whose mean curvature is zero. As such, maximal surfaces in Lorentzian geometry are directly analogous to minimal surfaces in Riemannian geometry. The difference in terminology between the two settings has to do with the fact that small regions in maximal surfaces are local maximizers of the area functional, while small regions in minimal surfaces are local minimizers of the area functional.
Katrin Leschke is a German mathematician specialising in differential geometry and known for her work on quaternionic analysis and Willmore surfaces. She works in England as a reader in mathematics at the University of Leicester, where she also heads the "Maths Meets Arts Tiger Team", an interdisciplinary group for the popularisation of mathematics, and led the "m:iv" project of international collaboration on minimal surfaces.
