Volume 35, Issue 2
On Conformal Metrics with Constant $Q$-Curvature

Anal. Theory Appl., 35 (2019), pp. 117-143.

Published online: 2019-04

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• 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.

• Keywords

Geometric PDEs, variational methods, min-max schemes.

35B33, 35J35, 53A30, 53C21

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@Article{ATA-35-117, author = {}, title = {On Conformal Metrics with Constant $Q$-Curvature}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0012}, url = {http://global-sci.org/intro/article_detail/ata/13110.html} }
TY - JOUR T1 - On Conformal Metrics with Constant $Q$-Curvature JO - Analysis in Theory and Applications VL - 2 SP - 117 EP - 143 PY - 2019 DA - 2019/04 SN - 35 DO - http://doi.org/10.4208/ata.OA-0012 UR - https://global-sci.org/intro/article_detail/ata/13110.html KW - Geometric PDEs, variational methods, min-max schemes. AB -

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.

Andrea Malchiodi. (2020). On Conformal Metrics with Constant $Q$-Curvature. Analysis in Theory and Applications. 35 (2). 117-143. doi:10.4208/ata.OA-0012
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