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The Journal of Differential Geometry is a peer-reviewed scientific journal of mathematics published by International Press on behalf of Lehigh University in 3 volumes of 3 issues each per year. The journal publishes an annual supplement in book form called Surveys in Differential Geometry. It covers differential geometry and related subjects ...
e. Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity.
Joel Spruck (born 1946 [1]) is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. [2] He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971. [3]
The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δ x (pronounced delta x ). The differential dx represents an infinitely small change in the variable x.
Riemannian manifold. In differential geometry, a Riemannian manifold or Riemannian space (M, g), so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p. The family gp of inner products is called a Riemannian metric (or ...
Connection (mathematics) In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data ...
Gerhard Huisken (born 20 May 1958) 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.
The analogous definition applies in the case of the Monge patches of the other two forms. ... for any Monge patch (u, v) ↦ (u, v, h(u, v)) whose range includes p, n is a multiple of (∂h / ∂u, ∂h / ∂v, −1) as evaluated at the point (p 1, p 2). The analogous definition applies in the case of the Monge patches of the other two forms.