Papers and Preprints

(Authors are always in alphabetical order.)

Square packings and rectifiable doubling measures
(Joint with
Matthew Badger)
Submitted.
arxiv

Uniformly rectifiable metric spaces: Lipschitz images, BiLateral Weak Geometric Lemma and Corona Decompositions
(Joint with
David Bate and
Matthew Hyde)
Submitted.
arxiv

Iterating the BigPieces operator and larger sets
(Joint with
Jared Krandel)
Bulletin of the London Mathematical Society, 54: 21512161.
arxiv

Lower bounds on mapping content and quantitative factorization through trees
(Joint with
Guy C. David)
Journal of the London Mathematical Society, 106 (2022), no. 2, 11701188.
arxiv

Quantitative decompositions of Lipschitz mappings into metric spaces
(Joint with
Guy C. David)
Transactions of the American Mathematical Society, 376 (2023), no. 8, 55215571.
arxiv
Zoom Talk by Guy C. David on this paper.

A sharp necessary condition for rectifiable curves in metric spaces
(Joint with
Guy C. David)
Revista Matematica Iberoamericana, 7 (2021), no. 3, 10071044
arxiv

An Analyst's Traveling Salesman Theorem for sets of dimension larger
than one
(Joint with
Jonas Azzam)
Mathematische Annalen, 370(3), 13891476
(2018). https://doi.org/10.1007/s0020801716090
Link
arxiv

The Analyst's traveling salesman theorem in graph inverse limits
(Joint with
Guy C. David)
Ann. Acad. Sci. Fenn. Math. 42 (2017), 649692.
arxiv

Multiscale analysis of 1rectifiable measures II: characterizations
(Joint with
Matthew Badger)
Anal. Geom. Metr. Spaces. Volume 5, Issue 1 (Mar 2017).
arxiv

Two sufficient conditions for rectifiable measures.
(Joint with
Matthew Badger)
Proc. Amer. Math. Soc. 144 (2016), 24452454
arxiv

An upper bound for the length of a Traveling Salesman path in the Heisenberg group.
(Joint with
Sean Li)
Rev. Mat. Iberoam. 32 (2016), no. 2, 391417.
arxiv

Multiscale analysis of 1rectifiable measures: necessary conditions.
(Joint with
Matthew Badger)
Mathematische Annalen: Volume 361, Issue 3 (2015), Page 10551072
arxiv

The traveling salesman problem in the Heisenberg group: upper curvature bound.
(Joint with
Sean Li)
Trans. of the Amer. Math. Soc. Volume 368, Number 7, July 2016, Pages 45854620
arxiv

A quantitative metric differentiation theorem.
(Joint with
Jonas Azzam)
Proc. Amer. Math. Soc. vol. 142 (2014), pages 13511357.
arxiv

Hard Sard: Quantitative Implicit Function and Extension Theorems for Lipschitz Maps.
(Joint with
Jonas Azzam)
Geometric and Functional Analysis: Volume 22, Issue 5 (2012), Page 10621123.
arxiv

How to take shortcuts in Euclidean space: making a
given set into a short quasiconvex set.
(Joint with
Jonas Azzam)
Proc. London Math. Soc. (2012) 105 (2): 367392.
arxiv

A doubling measure on R^d can charge a rectifiable curve.
(Joint with
John Garnett
and
Rowan Killip)
Proc. Amer. Math. Soc. vol. 138 (2010), pages 16731679
arxiv
 Christina Sormani
and
Stefan Wenger
wrote a paper titled
`Weak Convergence and Cancellation'.
It has an appendix written by Stefan Wenger and myself.
Calculus of Variations and Partial Differential Equations: Volume 38, Issue 1 (2010) , Page 183.
arxiv

Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian.
(Joint with
Peter W. Jones
and
Mauro Maggioni)
Ann. Acad. Sci. Fenn. Math. vol. 35 (2010), pages 131174
arxiv

Manifold parametrizations by eigenfunctions of the Laplacian and heat kernels.
(Joint with
Peter W. Jones
and
Mauro Maggioni)
PNAS, vol. 105 no. 6 (2008), pages 18031808
here
is a draft in pdf format
(may contain some typos).
(this is an announcement of the results, and outline of proofs, which appear in full in the paper above)

BigPiecesofLipschitzImages Implies a Sufficient Carleson Estimate in a Metric Space
arxiv

BiLipschitz Decomposition of Lipschitz functions into a Metric space.
Revista Matemática Iberoamericana,
vol 25, no. 2. Pages 521531.
arxiv

AhlforsRegular Curves In Metric Spaces.
Ann. Acad. Sci. Fenn. Math. 32 (2007), 437460.
arxiv.

Analyst's Traveling Salesman Theorems. A Survey.
In the tradition of AhlforsBers, IV, Contemporary Math., vol. 432, pages 209220, AMS
pdf or
dvi
(similar to the final version).

Subsets of Rectifiable curves in Hilbert SpaceThe Analyst's TSP.
Journal d'Analyse Mathematique 103 (2007), 331375.
arxiv
(This paper is essentially the same as my PhD thesis)
