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.
31-lug-2023
Settore MAT/05 - Analisi Matematica
Matematica e Informatica
34
CR Yamabe problem; singular solutions; Einstein-Hilbert action
Scuola Normale Superiore
MALCHIODI, ANDREA
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/133102
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