id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
0z708w35p5f	Ethan Lane Addison	Generalizing Kähler Metrics of Poincaré Type	2022		.txt	text/plain	212	3	1	To relate the gnarling construction to the extremal setting, we prove a local perturbation result showing the existence of cscK gnarled metrics in Kähler classes near to that of a standard product metric on N \ X, providing a significant step towards developing more general openness properties for extremal gnarled metrics. We define and explore various properties of a generalization of Poincaré-type Kähler metrics defined on the complement of a complex hypersurface X embedded in an ambient Kähler manifold N. After motivating interest in a generalization, especially from the viewpoint of extremal Kähler geometry, we construct a distortion potential ψτ V christened the gnarl associated to the vector field V due to its simulation of flowing along level sets of τ in the direction of V upon approaching X. Key subexponential estimates are derived to relate the gnarled metric to a starting Poincaré-type metric, allowing us to prove statements about the volume and integrals of the curvatures of the gnarled metric.	cache/0z708w35p5f.txt	txt/0z708w35p5f.txt