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Showing 1 to 3 of 3 for “"Brunn-Minkowski inequality"”.
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Some arithmetic Ramsey problems and inverse theorems
… sets which satisfy the equality in Kemperman's inequality, answering a question asked by Kemperman in 1964. When the ambient group is compact, we also get a near equality version of the above result with a sharp exponent bound, which confirms conjectures by Griesmer and by Tao. A measure …
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Combinatorics and Metric Geometry
… of this thesis; the sharp stability of the Brunn-Minkowski inequality (BM). This celebrated theorem from the 19th century asserts that for bodies A,B $\subset$ $\mathbb{R}$$^{k}$, we have |A + B|$^{1/k}$ $\geq$ |A|$^{1/k}$ + |B|$^{1/k}$, where |$\cdot$| is the Lebesgue measure and A + B := …
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Combinatorial Problems with Geometric Flavour
… result for the classical Freiman--Bilu $2^k$-inequality (improved by Green--Tao) and a generalization of Freiman's $3k-4$ theorem to arbitrary dimension. For $\delta>0$ sufficiently small and $A\subset \mathbb{Z}^k$ with $|A+A|\le (2^k+\delta)|A|$, we show either $A$ is covered by …