11 citations · 15 across the 11 of their papers we have counts for
12 papers
Weak geometric lemma for ADR boundary of a uniform domain implies uniform rectifiability
Aritro Pathak
We resolve a conjecture of Guy David and Svitlana Mayboroda. We show that if is a uniform domain with -dimensional Ahlfors David regular boundary $E…
Ergodicity of a surgered flow on unit tangent bundle of hyperbolic surface
Aritro Pathak
Starting with a trivial periodic flow on , the unit tangent bundle of a genus two surface, we perform a Dehn-type surgery on the manifold around a tubular neighborhood…
Open intervals in sums and products of Cantor sets
Aritro Pathak
We give new arguments for sums and products of sufficient numbers of arbitrary central Cantor sets to produce large open intervals. We further discuss the same question for i…
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…
Difference sets in Quadratic Density Hales Jewett conjecture with 2 letters
Aritro Pathak
The Quadratic Density Hales Jewett conjecture with letters states that for large enough , every dense subset of contains a combinatorial line where the wil…
Marstrand type slicing statements in are false for the counting dimension
Aritro Pathak
We show that for separated subsets of , the natural Marstrand type slicing statements are false with the counting dimension that was used earlier by Moreira and Lima an…
A Marstrand type slicing theorem for subsets of with the mass dimension
Aritro Pathak
We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by G…
Sums of powers, and products of elements of the middle third Cantor set
Aritro Pathak
The questions of the measure and finding open intervals in certain sets of sums and products of elements of the middle third Cantor set (or a variant of it), have generated conside…
On certain partition bijections related to Euler's partition problem
Aritro Pathak
We give short elementary expositions of combinatorial proofs of some variants of Euler's partitition problem that were first addressed analytically by George Andrews, and later com…
Glaisher's Partition problem
Aritro Pathak
We generalize the well known Glaisher partition bijection result. For given positive integers n, d, both greater than 1, we provide a rich family of bijections between the set of p…
An elementary argument for the magnetic field outside a solenoid
Aritro Pathak
The evaluation of the magnetic field inside and outside a uniform current density infinite solenoid of uniform cross-section is an elementary problem in classical electrodynamics t…
On the electrostatic equilibrium of charges and cavities in a conductor
Aritro Pathak
We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and insi…