# Article

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Keywords:
monotone measure; monotonicity formula
Summary:
We give a sufficient condition for a curve $\gamma: \Bbb R \to \Bbb R^n$ to ensure that the $1$-dimensional Hausdorff measure restricted to $\gamma$ is locally monotone.
References:
[1] Allard W.K.: On the first variation of a varifold. Ann. Math. 95 (1972), 417--491. DOI 10.2307/1970868 | MR 0307015 | Zbl 0252.49028
[2] Černý R.: Local monotonicity of measures supported by graphs of convex functions. Publ. Mat. 48 (2004), 369--380. MR 2091010 | Zbl 1090.28004
[3] Černý R.: Local monotonicity of Hausdorff measures restricted to real analytic curves. submitted.
[4] Kolář J.: Non-regular tangential behaviour of a monotone measure. Bull. London Math. Soc. 38 (2006), 657--666. DOI 10.1112/S0024609306018637 | MR 2250758 | Zbl 1115.49031
[5] Preiss D.: Geometry of measures in $\Bbb R^n$: Distribution, rectifiability and densities. Ann. Math. 125 (1987), 537--643. DOI 10.2307/1971410 | MR 0890162
[6] Simon L.: Lectures on geometric measure theory. Proc. C.M.A., Australian National University, Vol. 3, 1983. MR 0756417 | Zbl 0546.49019

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