Normal and Integral Currents

1960/11/01 by Herbert Federer, Herbert Fédérer, Wendell H. Fleming · 64 citations
Computer Science · Engineering · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Fluid dynamics and aerodynamics studies #stochastic dynamics and bifurcation

paper · doi:10.2307/1970227

Cited by

• Integral geometry in homogeneous spaces
• An integral formula for total gradient variation
• Anisotropic minimal surface equation with Dirichlet boundary condition
• The area minimizing problem in conformal cones
• Collapsing topology of isolated singularities
• Neural Representation of Minimal Surfaces
• Geometry of the Atomic Condition
• Conformal composition operators with applications to Dirichlet eigenvalues
• Riesz potential estimates under co-canceling constraints
• Detect duality obstruction of calibrations in smooth category
• Minimal hypersurfaces and geometric inequalities
• Currents in Heisenberg groups
• Cheeger constant, p-Laplacian, and Gromov-Hausdorff convergence
• The existence of extremal functions for discrete Sobolev inequalities on lattice graphs
• On smooth approximation of integral cycles mod 2
• Time-periodic branched transport
• Boundary case of equality in optimal Loewner-type inequalities
• An Asymmetric Affine Pólya--Szegö Principle
• The isoperimetric inequality for a minimal submanifold in Euclidean space
• Uniqueness of blowups and Lojasiewicz inequalities
• Compactness for manifolds and integral currents with bounded diameter and volume
• On fast computation of finite-time coherent sets using radial basis functions
• Rectifiability; a survey
• Brill-Lindquist-Riemann sums and their limits
• Boundary Regularity of Minimal Oriented Hypersurfaces on a Manifold
• Cubical Covers of Sets in ℝⁿ
• Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
• The weak convergence of varifolds generated by rectifiable flat G-chains
• Some configuration results for area-minimizing cones
• On FKM isoparametric hypersurfaces in \mathbbSⁿ × \mathbbSⁿ and new area-minimizing cones
• Uniqueness in the Plateau problem for calibrated currents
• Metric Convergence of Sequences of Static Spacetimes with the Null Distance
• Classification of geometrical objects by integrating currents and functional data analysis. An application to a 3D database of Spanish child population
• Sharp affine weighted L^p Sobolev type inequalities
• The Space-Time Connectivity Theorem for Normal Currents
• Higher divergence for nilpotent groups
• Semicontinuity of eigenvalues under intrinsic flat convergence
• On Plateau's Problem for Soap Films with a Bound on Energy
• On static three-manifolds with positive scalar curvature
• Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound
• Isoperimetric inequalities of euclidean type in metric spaces
• Croissance des boules et des géodésiques fermées dans les nilvariétés
• High-dimensional fillings in Heisenberg groups
• Mass Lower Bounds for Asymptotically Locally Flat Manifolds
• Soap Film Solutions to Plateau's Problem
• A surprising threshold for the validity of the method of singular projection
• Bott-Chern homology, Bott-Chern differential cohomology and the Hodge conjecture
• The Hasse Principle for Geometric Variational Problems: An Illustration via Area-minimizing Submanifolds
• Beyond Turing: Memory-Amortized Inference as a Foundation for Cognitive Computation
• Applications of Differential Chains to Complex Analysis and Dynamics
• On the Sormani-Wenger Intrinsic Flat Convergence of Alexandrov Spaces
• Non-Euclidean isoperimetric inequalities for nilpotent Lie groups
• Structure of Metric 1-currents: approximation by normal currents and representation results
• On the equality between the infimum obtained by solving various Plateau's problem
• Min-max theory and minimal surfaces with prescribed genus
• Homological Dehn functions of groups of type FP₂
• Intrinsic flat stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• Interaction energy between vortices of vector fields on Riemannian surfaces
• Explicit Determination in \Bbb R^N of (N-1)-Dimensional Area Minimizing Surfaces with Arbitrary Boundaries
• Solution of the Kirchhoff-Plateau Problem. [europepmc]
• Energy Minimisers with Prescribed Jacobian. [europepmc]
• Sharp Sobolev Inequalities via Projection Averages. [europepmc]
• Space-time integral currents of bounded variation. [europepmc]
• Classifying organisms and artefacts by their outline shapes [europepmc]