differential geometry, Mikhail Gromov's filling area conjecture asserts that the hemisphere has minimum area among the orientable surfaces that fill a...

inequality can be thought of as an "opposite" isoperimetric inequality. Filling area conjecture Gromov's systolic inequality for essential manifolds Gromov's inequality...

Gromov's filling area conjecture has been proved in a hyperelliptic setting (see reference by Bangert et al. below). The filling area conjecture asserts...

circles Riemannian circles, especially in connection with the filling area conjecture in Riemannian geometry, but this term has also been used for other...

Hyperellipticity of genus-2 curves was used to prove Gromov's filling area conjecture in the case of fillings of genus =1. Hyperelliptic curves of given genus g...

period, the integral curve is closed. The filling area conjecture, that a hemisphere has the minimum area among shortcut-free surfaces in Euclidean space...

relies on the Grushko decomposition theorem. see Gromov (1983) Filling area conjecture Gromov's inequality (disambiguation) Gromov's inequality for complex...

In Riemannian geometry, the filling area conjecture states that the hemisphere is the optimal (least area) isometric filling of the Riemannian circle. Remarkably...

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

{InjRad} M}{2(\dim M+2)}}.} Filling area conjecture Gromov's systolic inequality for essential manifolds Gromov, M.: Filling Riemannian manifolds, Journal...

systolic inequality for essential manifolds Essential manifold Filling radius Filling area conjecture Bolza surface First Hurwitz triplet Hermite constant Systoles...

The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional...

geodesic on an American football illustrating the proof of Gromov's filling area conjecture in systolic geometry, in the hyperelliptic case (see explanation)...

Riemannian metric of positive scalar curvature, which had been a major conjecture previously resolved by Schoen and Yau in low dimensions. In 1981, Gromov...

geometry Bangert, V.; Croke, C.; Ivanov, S.; Katz, M. (2005). "Filling area conjecture and ovalless real hyperelliptic surfaces". Geometric and Functional...

the area of the structure by 0.2% compared with the corresponding polyhedral structure. Although Kelvin did not state it explicitly as a conjecture, the...

the graph; the Hadwiger conjecture states that this is always at least as large as the chromatic number. The Hadwiger conjecture in combinatorial geometry...

spaces are sometimes used to provide examples or counterexamples to conjectures about topological spaces in general. Every manifold has a natural topology...

measured. Other related figures involve the construction of polyhedra, space-filling and honeycombs, polycubes, as well as cubes in compounds, spherical, and...

Kelvin's conjecture on minimal foams" probably referring to Gabbrielli, Ruggero (August 2009). "A new counter-example to Kelvin's conjecture on minimal...

mathematicians) of some of the circumstances surrounding the proof of the Poincaré conjecture, one of the most important accomplishments of 20th and 21st century mathematics...

Voronoi's conjecture on parallelohedra". European Journal of Combinatorics. 20 (6): 527–549. doi:10.1006/eujc.1999.0294. MR 1703597.. Voronoi conjectured that...

the Kepler conjecture). He also investigated the sphere packing problem. He was the first to show, in 1953, that proof of the Kepler conjecture can be reduced...

Euclidean plane and, more generally, the notion of a filling area function that estimates the area of a minimal surface in a Riemannian manifold in terms...

Attila Bölcskei calls this three-dimensional tiling the Rogers filling. He conjectures that, in any dimension greater than three, there is again a unique...

032<{\mathcal {H}}^{d}(S)<0.6} , but its exact value is unknown. It is conjectured that 0.528 < H d ( S ) < 0.590 {\displaystyle 0.528<{\mathcal {H}}^{d}(S)<0...

by replacing certain triples of faces by indentations. According to a conjecture of Branko Grünbaum, for every polyhedron that is topologically a sphere...

conjectures of André Weil in algebraic geometry opened up new areas of research. That Ramanujan conjecture is an assertion on the size of the tau-function, which...

area. The tetrastix and Weaire–Phelan structures have the same group of symmetries. Although this cube tiling includes some cubes (the ones filling the...

the value of the optimal packing fraction is a corollary of the Kepler conjecture: it can be achieved by putting a rhombicuboctahedron in each cell of the...