The paper gives a complete Weyl tensor description for 4D hypersurfaces yielding a new isoparametric characterization, plus sharp Euler-characteristic bounds on the Weyl functional and second fundamental form norm for minimal constant-scalar-curvature cases in space forms.
Q-Curvature and Poincare Metrics
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
This article presents a new definition of Branson's Q-curvature in even-dimensional conformal geometry. We derive the Q-curvature as a coefficient in the asymptotic expansion of the formal solution of a boundary problem at infinity for the Laplacian in the Poincare metric associated to the conformal structure. This gives an easy proof of the result of Graham-Zworski that the log coefficient in the volume expansion of a Poincare metric is a multiple of the integral of the Q-curvature, and leads to a definition of a non-local version of the Q-curvature in odd dimensions.
fields
math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Topological and rigidity results for four-dimensional hypersurfaces in space forms
The paper gives a complete Weyl tensor description for 4D hypersurfaces yielding a new isoparametric characterization, plus sharp Euler-characteristic bounds on the Weyl functional and second fundamental form norm for minimal constant-scalar-curvature cases in space forms.