Normal and integral currents
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Publication:2536545
DOI10.2307/1970227zbMath0187.31301OpenAlexW2028258142WikidataQ56851346 ScholiaQ56851346MaRDI QIDQ2536545
Herbert Federer, Wendell H. Fleming
Publication date: 1960
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1970227
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I, The viscosity method for min-max free boundary minimal surfaces, \(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation, Applications of \(p\)-harmonic transplantation for functional inequalities involving a Finsler norm, The Lawson-Simons' theorem on warped product submanifolds with geometric information, Monotonicity and symmetry of positive solution for 1-Laplace equation, Penrose-type inequalities with a Euclidean background, Strict convergence with equibounded area and minimal completely vertical liftings, Nonexistence of stable currents, A topological sphere theorem for contact CR-warped product submanifolds of an odd-dimensional unit sphere, Counterexamples to isosystolic inequalities, Functional capacities on the Grushin space \({\mathbb {G}}^n_\alpha \), Partial regularity of energy minimizing harmonic maps into a complete manifold, Min-max minimal hypersurfaces with obstacle, On the structure of flat chains modulo \(p\), Homology of contact 3-CR-submanifolds of an almost 3-contact hypersurface, Sequential warped product submanifolds having holomorphic, totally real and pointwise slant factors, Homotopy and homology vanishing theorems and the stability of stochastic flows, Besicovitch-Federer projection theorem for continuously differentiable mappings having constant rank of the Jacobian matrix, Soap films and covering spaces, A noninequality for the fractional gradient, An optimal Sobolev embedding for \(L^1\), Density of bounded maps in Sobolev spaces into complete manifolds, Local Sobolev constant estimate for integral Ricci curvature bounds, BV-ellipticity and lower semicontinuity of surface energy of Caccioppoli partitions of \(\mathbb{R}^n\), Velocities, stresses and vector bundle valued chains, Minimal surfaces and weak gravity, Stability of graphical tori with almost nonnegative scalar curvature, Almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds with spherical symmetry, Quantitative nonorientability of embedded cycles, Flat chains of finite size in metric spaces, Null homology in warped product Lagrangian submanifolds of the nearly Kaehler \(\mathbb{S}^6\) and its applications, Sewing Riemannian manifolds with positive scalar curvature, The singular structure and regularity of stationary varifolds, A mountain pass theorem for minimal hypersurfaces with fixed boundary, Supervised classification of geometrical objects by integrating currents and functional data analysis, An existence theorem for Brakke flow with fixed boundary conditions, Topological singular set of vector-valued maps. I: Applications to manifold-constrained Sobolev and BV spaces, Symmetric gradient Sobolev spaces endowed with rearrangement-invariant norms, Liftings, Young measures, and lower semicontinuity, A direct approach to the anisotropic Plateau problem, Real rectifiable currents, holomorphic chains and algebraic cycles, Weyl law for the volume spectrum, The existence of extremal functions for discrete Sobolev inequalities on lattice graphs, Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian, Complemented Brunn-Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures, Sharp Sobolev inequalities in Lorentz spaces for a mean oscillation, Higher-order Sobolev embeddings and isoperimetric inequalities, Boundary regularity of mass-minimizing integral currents and a question of Almgren, The graphs of Lipschitz functions and minimal surfaces on Carnot groups, Uniqueness of area minimizing surfaces for extreme curves, The longest shortest fence and sharp Poincaré-Sobolev inequalities, The nonlinear stability of rotationally symmetric spaces with low regularity, On Plateau's problem for soap films with a bound on energy, Isoperimetric inequality in the Grushin plane, The resolution of the Yang-Mills plateau problem in super-critical dimensions, On the nonexistence of stable currents in submanifolds of a Euclidean space, Filling invariants of stratified nilpotent Lie groups, Abundance of minimal surfaces, Plato's cave and differential forms, Filling functions of arithmetic groups, The \(L^p\) Gagliardo-Nirenberg-Zhang inequality, A generalized tetrahedral property, Higher-order compact embeddings of function spaces on Carnot-Carathéodory spaces, Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature, Sobolev embeddings, rearrangement-invariant spaces and Frostman measures, Topological singular set of vector-valued maps. 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