In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive...

derivative of the Wronskian of H and r from Sturm–Liouville theory. Cartan–Hadamard theorem Berger 2004; Jost, Jürgen (1997), Nonpositive curvature: geometric...

has everywhere non-positive sectional curvature. By Cartan–Hadamard theorem all Cartan–Hadamard manifolds are diffeomorphic to the Euclidean space R...

fixed point theorem). The basic result for a non-positively curved manifold is the Cartan–Hadamard theorem. The analog holds for a Hadamard space: a complete...

In mathematics, the Cartan–Hadamard conjecture is a fundamental problem in Riemannian geometry and geometric measure theory which states that the classical...

theory Cartan–Ambrose–Hicks theorem Cartan–Brauer–Hua theorem Cartan–Dieudonné theorem Cartan–Hadamard manifold Cartan–Hadamard theorem Cartan–Iwahori...

) Many of these results are sometimes called "Hadamard's theorem". Cartan–Hadamard theorem, a statement in Riemannian geometry concerning the structure...

(riemannian geometry) Bonnet theorem (differential geometry) Carathéodory–Jacobi–Lie theorem (symplectic topology) Cartan–Hadamard theorem (Riemannian geometry)...

topological restrictions (such as the Cheeger–Gromoll soul theorem or Cartan–Hadamard theorem) on geodesically complete Riemannian manifolds of positive...

Jacobi fields, the Morse index, the Rauch comparison theorems, and the Cartan–Hadamard theorem. Then it ascends to complex manifolds, Kähler manifolds...

topics in mathematics: Hadamard space, a geodesically complete metric space of non-positive curvature Cartan-Hadamard theorem, a result on the topology...

with sectional curvature K ≥ C, diameter ≤ D and volume ≥ V. The Cartan–Hadamard theorem states that a complete simply connected Riemannian manifold M with...

and was succeeded by Otto Blumenthal. Prime-counting function Cartan–Hadamard theorem Riemann–von Mangoldt formula Von Mangoldt function Hans Carl Friedrich...

Gauss–Bonnet theorem Hopf–Rinow theorem Cartan–Hadamard theorem Myers theorem Rauch comparison theorem Morse index theorem Synge theorem Weinstein theorem Toponogov...

v) to (x,expx v) is a diffeomorphism from TX onto X × X by the Cartan-Hadamard theorem. Let δ(s) be another geodesic parametrised by arclength through...

f_{p}(x)=\operatorname {dist} ^{2}(p,x)} is 1-convex. In 1928, Élie Cartan proved the Cartan–Hadamard theorem: if M is a complete manifold with non-positive sectional...

aspherical. In the case of Riemannian manifolds, this follows from the Cartan–Hadamard theorem, which has been generalized to geodesic metric spaces by Mikhail...

S} is a local diffeomorphism (in fact a covering map, by Cartan-Hadamard theorem), therefore, it induces an inner product in the tangent space of...

Godement-type integrals, whose combinatorics is governed by that of the Cartan-Helgason theorem for U/K0. An equivalent computation that arises in the theory of...

(t)-p|-t).} Cartan connection Cartan-Hadamard space is a complete, simply-connected, non-positively curved Riemannian manifold. Cartan–Hadamard theorem is the...

_{1}(M)} is the fundamental group of M. This is a consequence of the Cartan–Hadamard theorem. An infinite lens space L ( ∞ , q ) {\displaystyle L(\infty ,q)}...

holds for bounded sets S {\displaystyle S} in Hadamard manifolds, which has become known as the Cartan–Hadamard conjecture. In dimension 2 this had already...

then be deduced from the Bruhat-Tits fixed point theorem. Indeed, any bounded closed set in a Hadamard space is contained in a unique smallest closed ball...

such as the Gauss–Bonnet theorem, the uniformization theorem, the von Mangoldt-Hadamard theorem, and the embeddability theorem. There are other important...

three-dimensional Euclidean space admits at least two umbilical points. Cartan–Hadamard conjecture: can the classical isoperimetric inequality for subsets...

several mathematicians, including Georges Valiron, George Pólya, Jacques Hadamard and others, giving his return address as only "57 Grande rue, Saint-Maurice"...

metric spaces are CAT(0) groups, as a consequence of the metric Cartan-Hadamard theorem. This includes groups whose Dehn complex can wear a piecewise-euclidean...

established the 2-dimensional case of what later became known as the Cartan–Hadamard conjecture. He discovered that the so-called Weil representation, previously...

Carpenter Cartan–Kähler theorem – Élie Cartan, Erich Kähler Casimir effect – Hendrik Casimir Catalan's conjecture (a.k.a. Mihăilescu's theorem), Catalan...

Borel–Carathéodory theorem Corona theorem Hadamard three-circle theorem Hardy space Hardy's theorem Maximum modulus principle Nevanlinna theory Paley–Wiener theorem Progressive...