Publications Influence

Share This Author

## Nonlinear Potential Theory of Degenerate Elliptic Equations

- J. Heinonen, T. Kilpeläinen, O. Martio
- Mathematics
- 28 January 1993

Introduction. 1: Weighted Sobolev spaces. 2: Capacity. 3: Supersolutions and the obstacle problem. 4: Refined Sobolev spaces. 5: Variational integrals. 6: A-harmonic functions. 7: A superharmonic… Expand

## Quasiconformal maps in metric spaces with controlled geometry

- J. Heinonen, P. Koskela
- Mathematics
- 1 September 1998

This paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry. The principal message is that such a theory is both… Expand

## Lectures on Analysis on Metric Spaces

- J. Heinonen
- Mathematics
- 21 December 2000

1. Covering Theorems.- 2. Maximal Functions.- 3. Sobolev Spaces.- 4. Poincare Inequality.- 5. Sobolev Spaces on Metric Spaces.- 6. Lipschitz Functions.- 7. Modulus of a Curve Family, Capacity, and… Expand

## Uniformizing Gromov hyperbolic spaces

- M. Bonk, J. Heinonen, P. Koskela
- Mathematics
- 2001

— The unit disk in the complex plane has two conformally related lives: one as an incomplete space with the metric inherited from R 2 , the other as a complete Riemannian 2-manifold of constant… Expand

## Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients

- J. Heinonen, P. Koskela, N. Shanmugalingam, J. Tyson
- Mathematics
- 5 February 2015

Preface 1. Introduction 2. Review of basic functional analysis 3. Lebesgue theory of Banach space-valued functions 4. Lipschitz functions and embeddings 5. Path integrals and modulus 6. Upper… Expand

## NONSMOOTH CALCULUS

- J. Heinonen
- Mathematics
- 2005

We survey recent advances in analysis and geometry, where first order differential analysis has been extended beyond its classical smooth settings. Such studies have applications to geometric… Expand

## Quasiregular maps on Carnot groups

- J. Heinonen, I. Holopainen
- Mathematics
- 1 March 1997

In this paper we initiate the study of quasiregular maps in a sub-Riemannian geometry of general Carnot groups. We suggest an analytic definition for quasiregularity and then show that nonconstant… Expand

## Sobolev classes of Banach space-valued functions and quasiconformal mappings

- J. Heinonen, P. Koskela, N. Shanmugalingam, J. Tyson
- Mathematics
- 1 December 2001

We give a definition for the class of Sobolev functions from a metric measure space into a Banach space. We give various characterizations of Sobolev classes and study the absolute continuity in… Expand

## Geometric branched covers between generalized manifolds

- J. Heinonen, S. Rickman
- Mathematics
- 15 June 2002

We develop a theory of geometrically controlled branched covering maps between metric spaces that are generalized cohomology manifolds. Our notion extends that of maps of bounded length distortion,… Expand

## Definitions of quasiconformality

- J. Heinonen, P. Koskela
- Mathematics
- 1 December 1995

SummaryWe establish that the infinitesimal “H-definition” for quasiconformal mappings on Carnot groups implies global quasisymmetry, and hence the absolute continuity on almost all lines. Our method… Expand

...

1

2

3

4

5

...