Measurable sets in [0,R]² avoiding upward right triangles of area 1/2 satisfy |A| = O_c(R²/(log R)^c) for c<1/4 with Ω(R log R) example; for fixed-area triangles the bound sharpens to c<1/2 using a hyperbolic trilinear smoothing inequality and scale induction.
Some combinatorial, geometric and set theoretic problems in measure theory
2 Pith papers cite this work, alongside 19 external citations. Polarity classification is still indexing.
2
Pith papers citing it
19
external citations · OpenAlex
fields
math.CA 2verdicts
UNVERDICTED 2representative citing papers
Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.
citing papers explorer
-
On hyperbolic corners and unit-area triangles in planar sets of large measure
Measurable sets in [0,R]² avoiding upward right triangles of area 1/2 satisfy |A| = O_c(R²/(log R)^c) for c<1/4 with Ω(R log R) example; for fixed-area triangles the bound sharpens to c<1/2 using a hyperbolic trilinear smoothing inequality and scale induction.
-
Joint upper Banach density, VC dimensions and Euclidean point configurations
Introduces joint upper Banach densities for plane sets and proves a cross-set distance realization theorem plus maximal VC dimension for families of scaled curve translates with non-vanishing curvature.