Mapping theory in metric spaces

January 9 to January 13, 2012

at the

American Institute of Mathematics, Palo Alto, California

organized by

Luca Capogna, Jeremy Tyson, and Stefan Wenger

This workshop, sponsored by AIM and the NSF, will be devoted to mappings between metric spaces. Recent years have witnessed remarkable advances on basic questions concerning uniqueness, extendability, embeddability, uniformization and extremality of mappings in a variety of regularity classes. A persistent source of complexity is the influence of the geometry of the target space: problems whose solution is straightforward in the scalar-valued case become more intricate for vector-valued targets, even more so in case the target is a (nonlinear) manifold or metric space. The purpose of this workshop is to bring together researchers with differing backgrounds and expertise to highlight common techniques and methods and leverage existing knowledge towards the successful resolution of interdisciplinary problems.

The main topics for the workshop are:

The workshop will focus on particular problems of contemporary importance such as: (i) the role of quasiconformal geometry in the uniqueness problem for vector-valued absolute minimizing Lipschitz extensions, (ii) the interplay between bi-Lipschitz embedding theory and the Lipschitz density problem for metric space-valued Sobolev mappings, (iii) rigidity and uniformization problems for bi-Lipschitz or quasisymmetric mappings between metric spaces, (iv) extremal problems for quasiconformal mappings and their connection to hyperelasticity.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email

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