In: Advances in Applied Clifford Algebras, 2015, vol. 25, no. 2, p. 453-485
|
In: Breast Cancer Research and Treatment, ///-
|
In: Foundations of Computational Mathematics, 2015, vol. 15, no. 6, p. 1357-1411
|
In: Mediterranean Journal of Mathematics, 2015, vol. 12, no. 4, p. 1397-1427
|
In: Bulletin of the London Mathematical Society, 2020, vol. 52, no. 3, p. 472–488
A theorem of Dorronsoro from the 1980s quantifies the fact that real‐valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last...
|
In: Annali di Matematica Pura ed Applicata (1923 -), 2020, vol. 199, no. 1, p. 147–186
We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1. Several auxiliary properties of quasiconformal mappings between subdomains of H1 are proven, including BMO estimates for the logarithm of the Jacobian. Applications of the Koebe theorem include diameter bounds for images of curves, comparison of...
|
In: Geometriae Dedicata, 2020, p. -
This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give a review of the complete classification of such groups up to quasi-isometries and we compare the quasi- isometric classification with the bi-Lipschitz classification. On the...
|
In: Journal of Functional Analysis, 2020, vol. 278, no. 6, p. 108403
We introduce a notion of differential of a Sobolev map between metric spaces. The differential is given in the framework of tangent and cotangent modules of metric measure spaces, developed by the first author. We prove that our notion is consistent with Kirchheim's metric differential when the source is a Euclidean space, and with the abstract differential provided by the first author when...
|
In: Advances in Mathematics, 2019, vol. 354, p. 106745
We study singular integral operators induced by 3-dimensional Calderón-Zygmund kernels in the Heisenberg group. We show that if such an operator is L2 bounded on vertical planes, with uniform constants, then it is also L2 bounded on all intrinsic graphs of compactly supported C1,α functions over vertical planes. In particular, the result applies to the operator R induced by the...
|
In: Monatshefte für Mathematik, 2014, vol. 174, no. 4, p. 599-616
|