This paper surveys some results regarding compactness properties of Liouville equa- tions, which were principally initiated in the seminal paper [6]. We will begin showing an alternative between compactness and blow-up depending on concentration properties of expo- nential terms, and after turn to a more precise quantization property. We will also treat more recent developments concerning higher-order equations in conformal geometry.
COMPACTNESS AND LIOUVILLE EQUATIONS
Malchiodi, Andrea
2020
Abstract
This paper surveys some results regarding compactness properties of Liouville equa- tions, which were principally initiated in the seminal paper [6]. We will begin showing an alternative between compactness and blow-up depending on concentration properties of expo- nential terms, and after turn to a more precise quantization property. We will also treat more recent developments concerning higher-order equations in conformal geometry.File in questo prodotto:
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