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.
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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.