Robert Černý
Local monotonicity of Hausdorff measures restricted to real analytic curves

Comment.Math.Univ.Carolin. 51,1 (2010) 37-56.

Abstract:We prove that the 1-dimensional Hausdorff measure restricted to a~simple real analytic curve $\gamma: \mathbb R \to \mathbb R^N$, $N \ge 2$, is locally 1-monotone.

Keywords: monotone measure, monotonicity formula
AMS Subject Classification: 53A10 49Q15 28A75

PDF