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<pre>SEMINARIO DI EQUAZIONI DIFFERENZIALI
Dipartimento di Matematica
Universita' degli Studi di Roma "Tor Vergata"
Martedi' 15 gennaio 2019, ore 14:30 Aula Dal Passo
Pierpaolo Esposito (Universita' di Roma 3)
Titolo: Log-determinants in conformal geometry
I will report on a recent result, in collaboration with A. Malchiodi,
concerning a four-dimensional PDE of Liouville type arising in
the theory of log-determinants in conformal geometry.
The differential operator combines a linear fourth-order part with a
quasi-linear second-order one. Since both have the same scaling
behavior, compactness issues are very delicate and even the "linear
theory" is problematic. For the log-determinant of the conformal
laplacian we succeed to show existence and uniqueness of fundamental
solutions, quantization property for non-compact solutions and existence
results via critical point theory.
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