TY - JOUR
T1 - Isoperimetric inequality on CR-manifolds with nonnegative Q0-curvature
AU - Wang, Yi
AU - Yang, Paul
N1 - Publisher Copyright:
© 2018 Scuola Normale Superiore. All rights reserved.
PY - 2018
Y1 - 2018
N2 - In this paper we study contact forms on the three-dimensional Heisenberg manifold with its standard CR structure. We discover that the Q0-curvature, introduced by Branson, Fontana and Morpurgo [3] on the CR three-sphere and then generalized to any pseudo-Einstein CR three-manifold by Case and Yang [6], controls the isoperimetric inequality on such a CR-manifold. As the first and important step to show this, we prove that the nonnegative Webster curvature at infinity implies that the metric is normal, which is analogous to the behavior on a Riemannian four-manifold.
AB - In this paper we study contact forms on the three-dimensional Heisenberg manifold with its standard CR structure. We discover that the Q0-curvature, introduced by Branson, Fontana and Morpurgo [3] on the CR three-sphere and then generalized to any pseudo-Einstein CR three-manifold by Case and Yang [6], controls the isoperimetric inequality on such a CR-manifold. As the first and important step to show this, we prove that the nonnegative Webster curvature at infinity implies that the metric is normal, which is analogous to the behavior on a Riemannian four-manifold.
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U2 - 10.2422/2036-2145.201601_011
DO - 10.2422/2036-2145.201601_011
M3 - Article
AN - SCOPUS:85068400477
SN - 0391-173X
VL - 18
SP - 343
EP - 362
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
JF - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
IS - 1
ER -