Duy-Minh Nhieu

Non-doubling Ahlfors measures, perimeter measures, and the characterization of the trace spaces of Sobolev functions in Carnot-Carathéodory spaces

Introduction Carnot groups The characteristic set

A Notable Family of Entire Intrinsic Minimal Graphs in the Heisenberg Group which are not Perimeter Minimizing

X

A partial solution of the isoperimetric problem for the Heisenberg group

-variation,

Properties of harmonic measures in the Dirichlet problem for nilpotent Lie groups of Heisenberg type

X

On the best possible character of the

-perimeter and surface measure Geometric estimates from above on CC balls for the perimeter measure Geometric estimates from below on CC balls for the perimeter measure Fine differentiability properties of Sobolev functions Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure The extension theorem for a Besov space with respect to a lower Ahlfors measure Traces on the boundary of

L^Q

(\epsilon,\delta)

norm in some a priori estimates for non-divergence form equations in Carnot groups

domains The embedding of

Mathematical analysis of the two-color partial rainbow options

B^p_\beta(\Omega,d\mu)

A Difference Equation Arising from Logistic Population Growth

into

Isoperimetric and Sobolev inequalities for Carnot‐Carathéodory spaces and the existence of minimal surfaces

L^q(\Omega,d\mu)