Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds (2009)
Heinonen, Juha, Keith, Stephen
We give a sufficient condition for a metric (homology) manifold to be locally bi-Lipschitz equivalent to an open subset in $\rn$. The condition is a Sobolev condition for a measurable coframe of flat...
Abstract. 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...
STRONGLY UNIFORM DOMAINS AND PERIODIC QUASICONFORMAL MAPS (2007)
Scientiarum Fennicae, Juha Heinonen, Shanshuang Yang
Abstract. An m-uniform domain in R n is, roughly, a domain such that any two maps from the i-sphere, 0 i m! n, into the domain can be homotoped to each other without going too far or too close to the...
Smooth quasiregular mappings with branching (2004)
We give an example of a -smooth quasiregular mapping in 3-space with nonempty branch set. Moreover, we show that the branch set of an arbitrary quasiregular mapping in n -space has Hausdorff...
The branch set of a quasiregular mapping (2003)
We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds. Other...
These notes form a slightly expanded version of the lectures that I
On the locally branched Euclidean metric gauge (2002)
Heinonen, Juha, Sullivan, Dennis
A metric gauge on a set is a maximal collection of metrics on the set such that the identity map between any two metrics from the collection is locally bi-Lipschitz. We characterize metric gauges...
Geometric branched covers between generalized manifolds (2002)
Heinonen, Juha, Rickman, Seppo
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,...
Lectures on Analysis on metric spaces / Juha Heinonen (2001)
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BLD-mappings in $W^{2,2}$ are locally invertible (2000)
Heinonen, Juha, Kilpeläinen, Tero
We prove that mappings of bounded length distortion are local homeomorphisms if they have -integrable weak second derivatives.
Definitions of quasiconformality (1995)
Heinonen, Juha, Koskela, Pekka
We 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...
Sobolev mappings with integrable dilatations (1993)
Heinonen, Juha, Koskela, Pekka
We show that each quasi-light mapping f in the Sobolev space W 1 n ( Ω , R n ) satisfying ¦ Df ( x )¦ n ≦ K ( x, f ) J ( x, f ) for almost every x and for some K ε L r ( Ω ), r > n -1, is open...
Asymptotic paths for subsolutions of quasilinear elliptic equations (1988)
Let u be an entire lower semicontinuous subsolution to the quasilinear elliptic equation div A(x ,∇ u )=0 in ℝ n . It is shown that if u is not bounded above, then there exists a path going to...
F-harmonic measure in a non-linear potential theory / (1986)
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