A measure zero universal differentiability set in the Heisenberg group

The Limit Set of the Handlebody Set Has Measure Zero

This note fixes a small gap in the proof in [4] that the limit set of the handlebody set has measure zero.

Fourier transform of a Gaussian measure on the Heisenberg group

An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.

Differentiability of Solutions for the Non-degenerate P-laplacian in the Heisenberg Group

We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.

Universal Measure Zero, Large Hausdorff Dimension, and Nearly Lipschitz Maps

We prove that each analytic set in R contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitzlike mappings of separable metric s...

The HRT Conjecture and the Zero Divisor Conjecture for the Heisenberg Group