- Z. M. Balogh, R. Monti and J. T.
Tyson, "Frequency of Sobolev and quasiconformal dimension
distortion", 36 pp.
- N. Garofalo and J. T. Tyson, "Riesz
potentials and p-superharmonic functions in Lie groups of
Heisenberg type", 18 pp.
- E. Durand-Cartagena and J. T. Tyson, "Rectifiable curves in Sierpinski carpets", 17 pp.
- Z. M. Balogh, R. Berger, R. Monti and J. T. Tyson, "Exceptional sets for self-similar fractals in Carnot groups", 26 pp.
- P. Hajlasz and J. T. Tyson, "Sobolev Peano
cubes", 17 pp.
- J. T. Tyson, "Global conformal Assouad dimension
in the Heisenberg group", 28 pp.
- Z. M. Balogh, J. T. Tyson and B. Warhurst,
"Sub-Riemannian vs. Euclidean dimension comparison and fractal
geometry in Carnot groups", 45 pp.
- J. P. D'Angelo and J. T. Tyson, "Sub-Riemannian
geodesics and curves with derivatives of constant norm", 18 pp.
- L. Capogna, S. D. Pauls and J. T. Tyson,
"Convexity and horizontal second fundamental forms for hypersurfaces
in Carnot groups", 21 pp.
- L. V. Kovalev and J. T. Tyson, "Hyperbolic
and quasisymmetric structure of hyperspaces", 15 pp.
- J. T. Tyson, "Bi-Lipschitz embeddings of
compacta hyperspaces", 23 pp.
- J. T. Tyson and J.-M. Wu, "Characterizations of
snowflake metric spaces", 19 pp.
- R. Kaufman, J. T. Tyson and J.-M. Wu, "Smooth
quasiregular maps with branching in R^n", 26 pp.
- J. T. Tyson, "Quasiconformal maps in metric
spaces: questions and conjectures", 18 pp.
- Z. M. Balogh and J. T. Tyson, "Hausdorff
dimensions of self-similar and self-affine fractals in the Heisenberg
group", 39 pp.
- Z. M. Balogh, R. Hofer-Isenegger and J. T.
Tyson, "Lifts of Lipschitz maps and horizontal fractals in the
Heisenberg group", 38 pp.
- J. T. Tyson and J.-M. Wu, "Quasiconformal dimensions
of self-similar fractals", 47 pp.
- J. T. Tyson, "Counterexamples to Tischler's strong form
of Smale's Mean Value Conjecture", 16 pp.
Smale's Mean Value Conjecture asserts that for every polynomial P of
degree d satisfying P(0)=0, there exists a critical point θ of P
for which |P(θ)/θ|≤K|P'(0)|, where K=(d-1)/d. A
stronger conjecture due to Tischler asserts that
|1/2-P(θ)/(θ⋅P'(0))|≤ K_1 for some critical point
θ, where K_1=1/2-1/d. We give examples of polynomials in each
degree d≥5 for which the conjecture fails. We also prove estimates
for certain weighted L^p-averages of the quantities
|1/2-P(θ)/(θ⋅P'(0)|.
- I. Holopainen, N. Shanmugalingam and J. T. Tyson,
"On the conformal Martin boundary of domains in metric spaces", 22 pp.
- Z. M. Balogh and J. T. Tyson, "Potential
theory in Carnot groups", 15 pp.
- Z. M. Balogh and J. T. Tyson, "Polar coordinates
in Carnot groups", 34 pp.
- J. T. Tyson, "Sharp weighted Young's
inequalities and Moser-Trudinger inequalities on groups of Heisenberg
type and Grushin spaces", 28 pp.
- Z. M. Balogh, J. J. Manfredi and J. T. Tyson,
"Fundamental solution for the Q-Laplacian and sharp Moser-Trudinger
inequality in Carnot groups", 15 pp.
- Z. M. Balogh, I. Holopainen and J. T. Tyson,
"Singular solutions, homogeneous norms, and quasiconformal
mappings on Carnot groups", 23 pp.
- P. Koskela, J. Onninen and J. T. Tyson,
"Quasihyperbolic boundary conditions and capacity: Hölder
continuity of quasiconformal mappings", 21 pp.
- P. Koskela, J. Onninen and J. T. Tyson,
"Quasihyperbolic boundary conditions and Poincaré domains", 22
pp.
- J. T. Tyson, "Metric and geometric
quasiconformality in Ahlfors regular Loewner spaces", 52
pp.
- P. Koskela, N. Shanmugalingam and J. T. Tyson,
"Dirichlet forms, Poincaré inequalities, and the Sobolev spaces
of Korevaar-Schoen", 19 pp.
- J. Heinonen, P. Koskela, N. Shanmugalingam and J.
T. Tyson, "Sobolev classes of Banach space-valued functions and
quasiconformal mappings", 39 pp.
- C. J. Bishop and J. T. Tyson, "Locally minimal
sets for conformal dimension", 17 pp.
- C. J. Bishop and J. T. Tyson, "Conformal
dimension of the antenna set", 6 pp.
- J. T. Tyson, "Analytic properties of locally
quasisymmetric mappings from Euclidean domains", 16 pp.
- J. T. Tyson, "Lowering the Assouad dimension by
quasiconformal mappings", 12 pp.
- J. T. Tyson, "Sets of minimal Hausdorff
dimension for quasiconformal mappings", 7 pp.
- J. T. Tyson, "Quasiconformality and quasisymmetry
in metric measure spaces", 18 pp.