scientific article

No author found.

Publication date: 27 April 2016

Full work available at URL: http://www.sciencedirect.com/science/book/9780128044896

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

rectifiable currents geometric measure theory Gauss space varifolds rectifiable sets Poincaré conjecture immiscible fluids isoperimetric theorems double bubble conjecture area-minimizing hypersurfaces Double Bubbles Kelvin conjecture oriented tangent cones Perelman proof

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry (53-01) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control (49-01)

Related Items

A class of weighted isoperimetric inequalities in hyperbolic space ⋮ A white noise approach to stochastic currents of Brownian motion ⋮ Extremal lifetimes of persistent cycles ⋮ Conditions for the finiteness of the moments of the volume of level sets ⋮ Area-minimizing cones over Grassmannian manifolds ⋮ The geometry of the triple junction between three fluids in equilibrium ⋮ Unnamed Item ⋮ Corrected curvature measures ⋮ Symmetry break in the eight bubble compaction ⋮ Does a central limit theorem hold for the \(k\)-skeleton of Poisson hyperplanes in hyperbolic space? ⋮ Isoperimetric rigidity and distributions of 1-Lipschitz functions ⋮ On the Steiner property for planar minimizing clusters. The isotropic case ⋮ Random colorings in manifolds ⋮ The ε-ε property and the boundedness of isoperimetric sets with different monomial weights ⋮ Variance-covariance from a metropolis chain on a curved, singular manifold ⋮ Symmetric double bubbles in the Grushin plane ⋮ The regularity theory for the area functional (in geometric measure theory) ⋮ Self-similar groups and holomorphic dynamics: renormalization, integrability, and spectrum ⋮ Weighted monotonicity theorems and applications to minimal surfaces of ℍⁿ and 𝕊ⁿ ⋮ Approaching the isoperimetric problem in \(H_{\mathbb{C}}^m\) via the hyperbolic log-convex density conjecture ⋮ An upper Minkowski dimension estimate for the interior singular set of area minimizing currents ⋮ On area-minimizing Pfaffian varieties ⋮ On the finiteness of the moments of the measure of level sets of random fields ⋮ On the Steiner property for planar minimizing clusters. The anisotropic case ⋮ The Brown measure of a family of free multiplicative Brownian motions ⋮ The Riemannian quantitative isoperimetric inequality ⋮ Quantitative estimates for the Bakry–Ledoux isoperimetric inequality II ⋮ Recovering the homology of immersed manifolds ⋮ The isoperimetric problem with density ⋮ Critical points of the solutions to the \(H_R =H_L\) surface equation ⋮ Sweepouts of closed Riemannian manifolds ⋮ Bit threads and holographic entanglement ⋮ Rigidity for the isoperimetric inequality of negative effective dimension on weighted Riemannian manifolds ⋮ The isoperimetric problem for a class of non-radial weights and applications ⋮ Area maximizing surfaces in Lorentzian spaces ⋮ Double bubbles on the real line with log-convex density ⋮ On the sharp interface limit of a model for phase separation on biological membranes ⋮ Cohomology of flat currents on definable pseudomanifolds ⋮ On different notions of calibrations for minimal partitions and minimal networks in \(\mathbb{R}^2\) ⋮ Some weighted isoperimetric problems on \({\mathbb{R}}^N_+\) with stable half balls have no solutions ⋮ The periodic orbit conjecture for steady Euler flows ⋮ Unnamed Item ⋮ Equality in the logarithmic Sobolev inequality ⋮ Large mass rigidity for a liquid drop model in 2D with kernels of finite moments ⋮ Nondegeneracy of standard double bubbles ⋮ Generalized compactness for finite perimeter sets and applications to the isoperimetric problem ⋮ Varifold solutions of the two-phase three-dimensional magnetohydrodynamic equations ⋮ On the existence and nonexistence of isoperimetric inequalities with different monomial weights ⋮ The Gaussian double-bubble and multi-bubble conjectures ⋮ Moment Conditions and Bayesian Non-Parametrics ⋮ Nonparametric Bayes subject to overidentified moment conditions