In geometric topology, the spherical space form conjecture (now a theorem) states that a finite group acting on the 3-sphere is conjugate to a group of...

solving the Poincare conjecture, though Perelman declined both awards. The Poincaré conjecture and the spherical space form conjecture are corollaries of...

equivalent to two simpler conjectures: the Poincaré conjecture and the spherical space form conjecture. The elliptization conjecture is a special case of Thurston's...

the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

"Manifold Destiny" (On The New Yorker article) Spherical space form conjecture Thurston elliptization conjecture Uniformization theorem "Fields Medals 2006"...

Lurie, 2008) Spherical space form conjecture (Grigori Perelman, 2006) Poincaré conjecture (Grigori Perelman, 2002) Geometrization conjecture, (Grigori Perelman...

conjecture, due to Srinivasa Ramanujan (1916, p. 176), states that Ramanujan's tau function given by the Fourier coefficients τ(n) of the cusp form Δ(z)...

spades: Spheres Hemisphere Spherical cap Spherical lune Spherical polygon Spherical sector Spherical segment Spherical wedge Spherical zone 3-sphere Affine...

constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of vector fields on hypersurfaces...

The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit...

In mathematics, a spherical 3-manifold M is a 3-manifold of the form M = S 3 / Γ {\displaystyle M=S^{3}/\Gamma } where Γ {\displaystyle \Gamma } is a finite...

state of affairs was highly marked in the various cases of the Poincaré conjecture, in which four different proof methods are applied. The dimension of a...

than the dimension of the space in which they lie? This question gives rise to the following conjecture: Kakeya set conjecture: Define a Besicovitch set...

the minimum possible surface area is a standard double bubble: three spherical surfaces meeting at angles of 120° on a common circle. The double bubble...

conjecture states that this is the highest density that can be achieved by any arrangement of spheres, either regular or irregular. This conjecture was...

source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new...

finite spherical triangles on a sphere of infinite radius), the spherical relation between the sides of a right triangle reduces to the Euclidean form of...

space Wirtinger inequality (2-forms) Gromov's systolic inequality for essential manifolds Essential manifold Filling radius Filling area conjecture Bolza...

4064/fm-1-1-93-104. Arutyunyants, G.; Iosevich, A. (2004), "Falconer conjecture, spherical averages and discrete analogs", in Pach, János (ed.), Towards a...

historians, notably Joseph Needham, to conjecture that Chinese astronomers were, after all, aware of the Earth's sphericity. The egg reference, however, was...

to prove several conjectures made by Macdonald about them. First fix some notation: R is a finite root system in a real vector space V. R+ is a choice...

1970 MIT notes The Adams conjecture I Johannes Ebert, The Adams Conjecture, after Edgar Brown Strunk, Florian. On motivic spherical bundles Is it true that...

(2007), 626–641. A proof of the Kneser–Poulsen Conjecture (1955) for hemispheres in spherical d-space for all d > 1 (joint work with Robert Connelly,...

problem for the wave equation in three space dimensions can be obtained from the corresponding solution for a spherical wave. The result can then be also used...

cusped manifolds. Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that...

functions on Euclidean space. This definition is mostly used when discussing analytic manifolds in algebraic geometry. The spherical Earth is navigated using...

Euclidean space if the sum of the reciprocals of p, q, and r equals 1, spherical space if that sum is greater than 1, and hyperbolic space if the sum...

container holding the spherical grains. When spheres are randomly added to a container and then compressed, they will generally form what is known as an...

mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved...