A. Pathak

works on

ahlfors-david regularity 1 bilateral weak geometric lemma 1 uniform domains 1 uniform rectifiability 1 weak geometric lemma 1

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math.DS2026

Marstrand type slicing statements in $Z^{2} \subset R^{2}$ are false for the counting dimension

Aritro Pathak

We show that for $1$ separated subsets of $R^{2}$ , the natural Marstrand type slicing statements are false with the counting dimension that was used earlier by Moreira and Lima an…

math.DS2025

Ergodicity in the linked twist map with oppositely oriented shears

Aritro Pathak

We reduce the earlier known optimal shear parameter for which ergodicity is established in the linked twist map with two linear shears in opposite sense, in the most general settin…

Marstrand type slicing statements in Z2⊂R2 are false for the counting dimension

Ergodicity in the linked twist map with oppositely oriented shears

Marstrand type slicing statements in $Z^{2} \subset R^{2}$ are false for the counting dimension