On Conformal Metrics with Constant $Q$-Curvature

Year:    2019

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 117–143

Abstract

We review some recent results in the literature concerning existence of conformal metrics with constant $Q$-curvature. The problem is rather similar to the classical Yamabe problem: however it is characterized by a fourth-order operator that might lack in general a maximum principle. For several years existence of geometrically admissible solutions was known only in particular cases. Recently, there has been instead progress in this direction for some general classes of conformal metrics.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-0012

Analysis in Theory and Applications, Vol. 35 (2019), Iss. 2 : pp. 117–143

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Geometric PDEs variational methods min-max schemes.

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