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Search: All articles in the CMB digital archive with keyword convex set

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1. CMB Online first

Schoen, Tomasz
On Convolutions of Convex Sets and Related Problems
We prove some results concerning covolutions, the additive energy and sumsets of convex sets and its generalizations. In particular, we show that if a set $A=\{a_1,\dots,a_n\}_\lt \subseteq \mathbb R$ has the property that for every fixed $1\leqslant d\lt n,$ all differences $a_i-a_{i-d}$, $d\lt i\lt n,$ are distinct, then $|A+A|\gg |A|^{3/2+c}$ for a constant $c\gt 0.$

Keywords:convex sets, additive energy, sumsets
Category:11B99

2. CMB 2006 (vol 49 pp. 536)

Dostál, Petr; Lukeš, Jaroslav; Spurný, Jiří
Measure Convex and Measure Extremal Sets
We prove that convex sets are measure convex and extremal sets are measure extremal provided they are of low Borel complexity. We also present examples showing that the positive results cannot be strengthened.

Keywords:measure convex set, measure extremal set, face
Categories:46A55, 52A07

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