Concentrated monotone measures with non-unique tangential behavior in R3

0368882 - MÚ 2012 RIV CZ eng J - Journal Article
Černý, R. - Kolář, Jan - Rokyta, M.
Concentrated monotone measures with non-unique tangential behavior in R3.
Czechoslovak Mathematical Journal. Roč. 61, č. 4 (2011), s. 1141-1167. ISSN 0011-4642. E-ISSN 1572-9141
Institutional research plan: CEZ:AV0Z10190503
Keywords : monotone measure * monotonicity formula * tangent measure
Subject RIV: BA - General Mathematics
Impact factor: 0.262, year: 2011
http://www.springerlink.com/content/4014x737737155mg/

We show that for every epsilon > 0 there is a set A in R3 such that the Hausdorff one dimensional measure restricted to A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and the measure has the 1-dimensional density between 1 and 2+epsilon everywhere in the support.
Permanent Link: http://hdl.handle.net/11104/0203098