We consider sone analytic problems arising in sub-Riemannian geometry. First, we construct singular solutions to the CR Yamabe equation in the Heisenberg group in two regimes: nearly cylindrical solutions via bifurcation theory and nearly locally spherical solutions via a refined implicit function argument. We then consider the Einstein-Hilbert action in the CR setting. We characterize stationary points as pseudo-Einstein structures, then showing the role of embeddability in determining the sign of the second variation at standard spheres.
Geometric aspects of PDEs on sub-Riemannan manifolds / Afeltra, Claudio; relatore: MALCHIODI, ANDREA; Scuola Normale Superiore, ciclo 34, 31-Jul-2023.
Geometric aspects of PDEs on sub-Riemannan manifolds
AFELTRA, CLAUDIO
2023
Abstract
We consider sone analytic problems arising in sub-Riemannian geometry. First, we construct singular solutions to the CR Yamabe equation in the Heisenberg group in two regimes: nearly cylindrical solutions via bifurcation theory and nearly locally spherical solutions via a refined implicit function argument. We then consider the Einstein-Hilbert action in the CR setting. We characterize stationary points as pseudo-Einstein structures, then showing the role of embeddability in determining the sign of the second variation at standard spheres.File | Dimensione | Formato | |
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