Analysis and geometry on pseudohermitian manifolds

November 6 to November 10, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

Sorin Dragomir, Howard Jacobowitz, and Paul Yang

Original Announcement

This workshop will be devoted to mathematical analysis and differential geometry on pseudohermitian manifolds. The analysis of solutions to the tangential Cauchy-Riemann equations is best performed in the presence of nondegeneracy assumptions on the given CR structure. For then a contact form $\theta$ may be chosen and differential geometric methods become available, for instance to compute CR invariants (e.g. the Chern-Moser tensor, or Kohn-Rossi cohomology) in terms of pseudohermtian invariants. An array of differential geometric objects (e.g. a sub-Riemannian structure along the maximally complex distribution together with the resulting Carnot-Caratheodory distance function, the Webster metric, the Tanaka-Webster connection embedding the subRiemannian geometry at hand into connection theory, the Fefferman metric bringing into the picture methods and results from Lorentzian geometry) spring naturally from $\theta$ and manifest either as sources of problems (e.g. the CR Yamabe problem, the existence and partial regularity problem for subelliptic harmonic maps from a CR manifold) or as geometric tools (e.g. the description of Cartan chains as projections of null geodesics of Fefferman's metric).

The workshop will concentrate on the following themes:

The workshop will attempt to gather researchers whose mains scientific interests are related to one or more of the following areas:
  1. analysis in several complex variables,
  2. theory of Hormander systems of vector fields and subelliptic partial differential equations,
  3. differential geometry on CR, pseudohermitian, and Lorentzian manifolds.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Chains in CR geometry as geodesics of a Kropina metric
by  Jih-Hsin Cheng, Taiji Marugame, Vladimir S. Matveev, and Richard Montgomery
On the Lichnerowicz conjecture for CR manifolds with mixed signature
by  Jeffrey S. Case, Sean N. Curry, and Vladimir S. Matveev