Browsing Mathematics by Author "Toro, Tatiana"
Now showing items 15 of 5

Analytic and geometric aspects of the elliptic measure on nonsmooth domains
Zhao, ZihuiHarmonic/elliptic measure arises naturally in probability and in the study of boundary value problems for elliptic operators. It has attracted the attention of many mathematicians to study the relationship between the ... 
Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications
Lewis, StephenIn this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ... 
Minkowskitype Estimates on the Quantitative Strata of the Generalized Critical set of Green's functions for TwoSided NTA Domains arising from a FreeBoundary Problem for Harmonic Measure
McCurdy, SeanIn this work, we prove three things. The main results are two different results on Minkowskitype estimates on the quantitative strata of the generalized critical set of Green's functions of 2Sided NTA domains arising ... 
On the Geometry of Rectifiable Sets with Carleson and Poincaretype inequlaities
Merhej, JessicaA central question in geometric measure theory is whether geometric properties of a set translate into analytical ones. In 1960, E. R. Reifenberg proved that if an $n$dimensional subset $M$ of $\mathbb{R}^{n+d}$ is well ... 
The geometry of uniform measures
Nimer, Abdalla DaliUniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. They were first studied in the groundbreaking work of Preiss where he proved that a Radon measure ...