Some elementary aspects of Hausdorff measure and dimension
Basic properties of Hausdorff content, dimension, and measure of subsets of metric spaces are discussed, especially in connection with Lipschitz mappings and topological dimension.
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arXiv subjects
Stephen Semmes
Publications and source records attributed to Stephen Semmes.
Calculus, fractals, and analysis on metric spaces
This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.
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Sums, rearrangements, and norms
These informal notes deal with a number of questions related to sums and integrals in analysis.
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Sums and averages
These informal notes are concerned with sums and averages in various situations in analysis.
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Ode to commutator operators
These brief remarks have been prepared in connection with a conference in honor of my thesis advisor, Richard Rochberg.
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Cellular structures, quasisymmetric mappings, and spaces of homogeneous type
A class of Cantor-type spaces and related geometric structures are discussed.
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An introduction to the geometry of ultrametric spaces
Some examples and basic properties of ultrametric spaces are briefly discussed.
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Elementary aspects of the geometry of metric spaces
The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.
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Another introduction to the geometry of metric spaces
Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.
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A geometric construction for fractal sets and related linear operators
A way to add an extra dimension is briefly discussed.
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Complementary self-similarity
A few aspects of self-similarity related to complementary components of closed subsets of R^n are briefly discussed.
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A few remarks about linear operators and disconnected open sets in the plane
Some aspects of analysis on disconnected open subsets of the plane with connected fractal boundary are discussed.
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An introduction to the geometry of metric spaces
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
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Quasi-fractal sets in space
The focus here is on connected fractal sets with topological dimension 1 and a lot of topological activity, and their connections with analysis.
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Some aspects of calculus on non-smooth sets
Sets in R^n in which every pair of elements x, y can be connected by a path in the set of length bounded by a constant multiple of the distance between x and y are considered.
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Some remarks about Clifford analysis and fractal sets
Although Clifford analysis is like complex analysis in many ways, there are obvious differences related to noncommutativity, and a few aspects of this are considered here.
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What is a metric space?
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
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A few remarks concerning complex-analytic metric spaces
The special case of closed subsets of C^n is briefly discussed.
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