Results 41 to 50 of about 2,662,283 (378)
, 1997 An earlier paper describes a program to prove the Kepler conjecture on sphere packings. This paper carries out the second step of that program. A sphere packing leads to a decomposition of $R^3$ into polyhedra. The polyhedra are divided into two classes.
Hales, Thomas C.
core +9 more sources
São Paulo Journal of Mathematical Sciences, 2018 Spheres can be written as homogeneous spaces $G/H$ for compact Lie groups in a small number of ways. In each case, the decomposition of $L^2(G/H)$ into irreducible representations of $G$ contains interesting information. We recall these decompositions, and see what they can reveal about the analogous problem for noncompact real forms of $G$ and $H$.
Schlichtkrull, Henrik +2 more
openaire +4 more sources
Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere [PDF]
, 2016 The four-dimensional (4D) Lorentz group $SL(2,\mathbb{C})$ acts as the two-dimensional (2D) global conformal group on the celestial sphere at infinity where asymptotic 4D scattering states are specified.
S. Pasterski +2 more
semanticscholar +1 more source
Affine sphere relativity [PDF]
, 2016 We investigate spacetimes whose light cones could be anisotropic. We prove the equivalence of the structures: (a) Lorentz-Finsler manifold for which the mean Cartan torsion vanishes, (b) Lorentz-Finsler manifold for which the indicatrix (observer space ...
Minguzzi, E.
core +2 more sources
The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere
Annales scientifiques de l'École Normale Supérieure, 2022 We extend the classification of Robert Bryant of Willmore spheres in $S^3$ to variational branched Willmore spheres $S^3$ and show that they are inverse stereographic projections of complete minimal surfaces with finite total curvature in $\mathbb{R}^3$ and vanishing flux. We also obtain a classification of variational branched Willmore spheres in $S^4$
Michelat, Alexis, Rivière, Tristan
openaire +2 more sources
The sphere packing problem in dimension 8The sphere packing problem in dimension 8 [PDF]
, 2016 In this paper we prove that no packing of unit balls in Euclidean space R-8 has density greater than that of the E8-lattice packing.
M. Viazovska
semanticscholar +1 more source
Cavity quantum electrodynamics with ferromagnetic magnons in a small yttrium-iron-garnet sphere [PDF]
npj Quantum Information, 2015 Hybridizing collective spin excitations and a cavity with high cooperativity provides a new research subject in the field of cavity quantum electrodynamics and can also have potential applications to quantum information.
semanticscholar +1 more source
Casimir Energy and Entropy in the Sphere--Sphere Geometry
, 2011 We calculate the Casimir energy and entropy for two spheres described by the perfect metal model, plasma model, and Drude model in the large separation limit.
Rodriguez-Lopez, Pablo
core +1 more source
Serbian Astronomical Journal, 2020 I review the origins and development of the idea of Dyson spheres, their purpose, their engineering, and their detectability. I explicate the ways in which the popular imagining of them as monolithic objects would make them dynamically unstable under gravity and radiation pressure, and mechanically unstable to buckling.
openaire +4 more sources
Willmore spheres in the $3$-sphere revisited
Communications in Analysis and Geometry, 2023 3 ...
openaire +2 more sources