Local monotonicity of measures supported by graphs of convex functions.
- Autores: Robert Cerný
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 48, Nº 2, 2004, págs. 369-380
- Idioma: español
- Enlaces
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Resumen
Let f ∈ C2 (R) satisfy f(0) = f 0 (0) = 0 and f 00(0) > 0. Then the 1-dimensional Hausdorff measure restricted to the graph of f is locally monotone near the origin in the sense that there exists σ > 0 such that the function r 7→ µf B(z,r) r is nondecreasing on (0, σ) for every centre z ∈ B(σ). The result is reformulated for Hausdorff measures restricted to uniformly C2 -curves in R 2 with the curvature bounded away from zero and infinity.
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