... Minimizing Currents.
50 years sets with positive reach -- a survey.
A characterization of graphs which can be approximated in area by smooth graphs
For vector valued maps, convergence in and of all minors of the Jacobian matrix in is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension can be approximated strongly in this sense by smooth maps if and only if the same property holds for the restriction to a.e. 2-dimensional plane intersecting the domain.
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...
A derivation formula for convex integral functionals defined on .
A Geometrical Theory of Multiple Integral Problems in the Calculus of Variations
A Geometrical Theory of Multiple Integral Problems in the Calculs of Variations (Short Communication)
A new proof of the compactness theorem for integral currents.
A new proof of the rectifiable slices theorem
This paper gives a new proof of the fact that a -dimensional normal current in is integer multiplicity rectifiable if and only if for every projection onto a -dimensional subspace, almost every slice of by is -dimensional integer multiplicity rectifiable, in other words, a sum of Dirac masses with integer weights. This is a special case of the Rectifiable Slices Theorem, which was first proved a few years ago by B. White.
A note on weak approximation of minors
A uniqueness theorem for Zn-periodic variational problems.
Allard type regularity results for varifolds with free boundaries
An a Priori Estimate for the Oscillation of the Normal to a Hypersurface Whose First and Second Variation With Respect to an Elliptic Integrand is Controlled.
An algebraic characterization of quasi-Möbius homeomorphisms. (Une caractérisation algébrique des homéomorphismes quasi-Möbius.)
An Embedding Theorem in the Calculus of Variations for Multiple Integrals.
An isoperimetric inequality in R3
Angular limits of double layer potentials
Approximation in Area of Graphs with Isolated Singularities.
Area-minimizing integral currents with movable boundary parts of prescribed mass
Asymptotically equal generalized distances: induced topologies and -energy of a curve.