Results 1 
9 of
9
A RANDOM WALK IN ANALYSIS
, 2011
"... Abstract. I discuss the impact various papers have had on my own work. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. I discuss the impact various papers have had on my own work.
An upper bound for the length of a Traveling Salesman path in the Heisenberg group
, 2014
"... ar ..."
(Show Context)
TWO SUFFICIENT CONDITIONS FOR RECTIFIABLE MEASURES
"... Abstract. We identify two sufficient conditions for locally finite Borel measures on Rn to give full mass to a countable family of Lipschitz images of Rm. The first condition, extending a prior result of Pajot, is a sufficient test in terms of Lp affine approximability for a locally finite Borel mea ..."
Abstract
 Add to MetaCart
Abstract. We identify two sufficient conditions for locally finite Borel measures on Rn to give full mass to a countable family of Lipschitz images of Rm. The first condition, extending a prior result of Pajot, is a sufficient test in terms of Lp affine approximability for a locally finite Borel measure µ on Rn satisfying the global regularity hypothesis lim sup r↓0 µ(B(x, r))/rm < ∞ at µa.e. x ∈ Rn to be mrectifiable in the sense above. The second condition is an assumption on the growth rate of the 1density that ensures a locally finite Borel measure µ on Rn with lim r↓0 µ(B(x, r))/r = ∞ at µa.e. x ∈ Rn is 1rectifiable. 1.
QUASICONFORMAL PLANES WITH BILIPSCHITZ PIECES AND EXTENSIONS OF ALMOST AFFINE MAPS
"... Abstract. A quasiplane f(V) is the image of an ndimensional Euclidean subspace V of RN (1 ≤ n ≤ N − 1) under a quasiconformal map f: RN → RN. We give sufficient conditions in terms of the weak quasisymmetry constant of the underlying map for a quasiplane to be a biLipschitz nmanifold and for a qu ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. A quasiplane f(V) is the image of an ndimensional Euclidean subspace V of RN (1 ≤ n ≤ N − 1) under a quasiconformal map f: RN → RN. We give sufficient conditions in terms of the weak quasisymmetry constant of the underlying map for a quasiplane to be a biLipschitz nmanifold and for a quasiplane to have big pieces of biLipschitz images of Rn. One main novelty of these results is that we analyze quasiplanes in arbitrary codimension N − n. To establish the big pieces criterion, we prove new extension theorems for “almost affine ” maps, which are of independent interest. This work is related to investigations by Tukia and Väisälä on extensions of quasisymmetric maps with small distortion. Contents
A DOUBLING MEASURE CAN CHARGE A RECTIFIABLE CURVE
, 906
"... Abstract. For d ≥ 2, we construct a doubling measure ν on R d and a rectifiable curve Γ such that ν(Γ)> 0. 1. ..."
Abstract
 Add to MetaCart
Abstract. For d ≥ 2, we construct a doubling measure ν on R d and a rectifiable curve Γ such that ν(Γ)> 0. 1.
A SUFFICIENT CONDITION FOR HAVING BIG PIECES OF BILIPSCHITZ IMAGES OF SUBSETS OF EUCLIDEAN SPACE IN HEISENBERG GROUPS
"... ar ..."
(Show Context)
Generalized Sines, Multiway Curvatures, and the Multiscale Geometry of dRegular Measures
, 2009
"... Many thanks to my advisor Gilad Lerman, especially for his clear vision of how this work was to proceed and his confidence in my ability to achieve it. I am fortunate to have had him as an advisor and a friend. Thanks also to the various faculty I’ve met at the U of M, such as Professors Paul Garret ..."
Abstract
 Add to MetaCart
(Show Context)
Many thanks to my advisor Gilad Lerman, especially for his clear vision of how this work was to proceed and his confidence in my ability to achieve it. I am fortunate to have had him as an advisor and a friend. Thanks also to the various faculty I’ve met at the U of M, such as Professors Paul Garrett and Dick Mcgehee, without whom I would definitely not have made it through graduate school. Special thanks also to Professors Sergey Bobkov, Peter Olver, and Guillermo Sapiro for being on my defense committee. Thanks to my family for helping me to be in a situation to accomplish such a thing, my mother for her support, my uncle for his example, my aunts for the encouragement, and especially my wife for her patience. Great thanks are also due to Charles Royals, a benefactor without whom my trajectory in life would have been fundamentally different. i Dedication The work is dedicated to two people. The first is Leon Faure at the College of San Mateo who saw me as a mathematician long before I myself did. I have tried to emulate his clear thinking and common sense in both my research and teaching. The second is my son