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- W3102286475 abstract "For a set $A$ of points in the plane, not all collinear, we denote by ${rm tr}(A)$ the number of triangles in any triangulation of $A$; that is, ${rm tr}(A) = 2i+b-2$ where $b$ and $i$ are the numbers of points of $A$ in the boundary and the interior of $[A]$ (we use $[A]$ to denote convex hull of $A$). We conjecture the following analogue of the Brunn-Minkowski inequality: for any two point sets $A,B subset {mathbb R}^2$ one has [ {rm tr}(A+B)^{frac12}geq {rm tr}(A)^{frac12}+{rm tr}(B)^{frac12}. ] We prove this conjecture in several cases: if $[A]=[B]$, if $B=Acup{b}$, if $|B|=3$, or if none of $A$ or $B$ has interior points." @default.
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- W3102286475 date "2019-08-29" @default.
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- W3102286475 title "Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane" @default.
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- W3102286475 doi "https://doi.org/10.1007/s00454-019-00131-9" @default.
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