For n compact sets in R^d each with Feng-Wu thickness >=c, their sum has non-empty interior once n exceeds sqrt(d)/(sqrt(1+c)-1)^2, improving the prior cubic dependence on 1/c to quadratic at the cost of a sqrt(d) factor.
Title resolution pending
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.MG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
An improved bound for sumsets of thick compact sets via the Shapley--Folkman theorem
For n compact sets in R^d each with Feng-Wu thickness >=c, their sum has non-empty interior once n exceeds sqrt(d)/(sqrt(1+c)-1)^2, improving the prior cubic dependence on 1/c to quadratic at the cost of a sqrt(d) factor.