Size of characteristic sets and functions with prescribed gradient

By Zoltán M. Balogh. 2003

152 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0f56227248e3673f875160a4a148e18c58f3b9fd

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Intrinsic curvature of curves and surfaces and a Gauss–Bonnet theorem in the Heisenberg group (2016, background): “For estimates of the size of the characteristic set, see [4].”
Minimal Surfaces in the Heisenberg Group (2001, background): “ither to B. Franchi, R. Serapioni and F. Serra Cassano ([FSSC99], see proposition 2.14) or L. Capogna, D. Daneilli and N. Garofalo ([CDG94b] p. 211). The reader should also consult Z. Balough’s paper [Bal] concerning various aspects of the perimeter measure for surfaces as well as a study of differe”
Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, unknown): “For Carnot groups one has the following sharper result first proved in codimension one by Balogh for the Heisenberg group [2], and subsequently extended to arbitrary Carnot groups and codimension by Magnani [69,70].”
Regular Hypersurfaces, Intrinsic Perimeter and Implicit Function Theorem in Carnot Groups (2003, background): “Balogh (see [ 5 ]) was the first one to prove that, in the Heisenberg groups, the intrinsic (Q − 1)-Hausdorff measure of the characteristic set of an Euclidean C1 surface vanishes.”
Regularity of C1 smooth surfaces with prescribed p-mean curvature in the Heisenberg group (2007, background): “For the study of the size of singular set, we refer the reader to [1] (in which singular set is called characteristic set).”
Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group (2004, unknown): “The more precise modulus of continuity of the gradient which we state and use here can, however, only be found at the end of the proof of this theorem in [4].”
Existence and uniqueness for P-area minimizers in the Heisenberg group (2006, methodology): “4 in [3] by a different argument (we used only elementary linear algebra and the implicit function theorem in the proof; also we were not aware of [1] at the time [3] was written).”
Regular submanifolds, graphs and area formula in Heisenberg groups (2007, background): “Balogh (see [6]) was the first one to prove that, in the Heisenberg groups, the intrinsic (Q − 1)-Hausdorff measure of the characteristic set of an Euclidean C1 surface vanishes.”