@misc{10481/102400,
year = {2024},
month = {11},
url = {https://hdl.handle.net/10481/102400},
abstract = {This paper deals with the question of prescribing the Gaussian curvature on a disk and the geodesic curvature of its boundary by means of a conformal
deformation of the metric. We restrict ourselves to a symmetric setting in which the
Gaussian curvature is negative, and we are able to give general existence results.
Our approach is variational, and solutions will be searched as critical points of an
associated functional. The proofs use a perturbation argument via the monotonicity trick of Struwe, together with a blow-up analysis and Morse index estimates.
We also give a nonexistence result that shows that, to some extent, the assumptions
required for existence are necessary.},
organization = {IMAG-Maria de Maeztu Excellence Grant CEX2020-001105-M},
organization = {Junta de Andalucía FQM-116. R.L.-S},
organization = {Juan de la Cierva In corporacion fellowship (JC2020-046123-I)},
organization = {European Union Next Generation EU/PRTR},
organization = {MICIN/AEI PID2021-122122NB I00, PRE2021-099898},
publisher = {Elsevier},
keywords = {Prescribed curvature problem},
keywords = {Conformal metric},
keywords = {Blow-up analysis},
keywords = {Variational methods},
title = {Prescribing curvatures in the disk via conformal changes of the metric: The case of negative Gaussian curvature},
doi = {10.1016/j.jde.2025.01.007},
author = {López Soriano, Rafael and Reyes Sánchez, Francisco Javier and Ruiz Aguilar, David},
}