Speakers
 Andrea Malchiodi
 SNS Pisa

A positive mass theorem in CR geometry
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Andrea Malchiodi
A positive mass theorem in CR geometry
We consider a class of CR manifolds which are defined as asymptotically Heisenberg,
and for these we give a notion of mass. From the solvability of the $\Box_b$ equation
in a certain functional class ([HsiaoYung]), we prove positivity of the mass under the
condition that the Webster curvature is positive and that the manifold is embeddable.
We apply this result to the Yamabe problem for compact CR manifolds, assuming positivity
of the Webster class and nonnegativity of the Paneitz operator. This is joint work with
J.H.Cheng and P.Yang.
 Roberto Monti
 Università di Padova

Recent results on the regularity of Hminimal surfaces
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Roberto Monti
Recent results on the regularity of Hminimal surfaces
We review some recent results on the regularity of Hminimal
boundaries in the Heisenberg group: Lipschitz approximation, height estimate,
and harmonic approximation. This is part of a joint research program with D. Vittone.
 Manuel Ritoré
 Universidad de Granada

MINI COURSE Variational formulas for the subRiemannian area in contact subRiemannian manifolds
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Manuel Ritoré
MINI COURSE Variational formulas for the subRiemannian area in contact subRiemannian manifolds
We derive variational formulas of the subRiemannian area in contact subRiemannian manifolds, introduce hypersurfaces with prescribed mean curvature, and discuss the regularity of C^1 surfaces (with prescribed mean curvature) in the 3dimensional case.

The Bernstein problem for C^1 surface in H^1
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Manuel Ritoré
The Bernstein problem for C^1 surface in H^1
We shall prove that an stable intrinsic graph of class C^1 in H^1 is a vertical plane. This is joint work with Matteo Galli.
 Paul Yang
 Princeton University

MINI COURSE Isoperimetric inequality in CR manifolds in 3D
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Paul Yang
MINI COURSE Isoperimetric inequality in CR manifolds in 3D
I plan to discuss the isoperimetric problem, in the Heisenberg space as well
as CR 3manifolds. I begin by reviewing the pseudohermitian geometry,
the local geometry of a surface. The problem of Pansu. A new fourth order
invariant called the Qprime curvature, and its relation to the isoperimetric
inequality.
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Isoperimetric inequality in CR manifolds in 3D
view abstract
Paul Yang
Isoperimetric inequality in CR manifolds in 3D
I plan to discuss the isoperimetric problem, in the Heisenberg space as well
as CR 3manifolds. I begin by reviewing the pseudohermitian geometry,
the local geometry of a surface. The problem of Pansu. A new fourth order
invariant called the Qprime curvature, and its relation to the isoperimetric
inequality.
download notes