2024/08/03 by Sevost'yanov, Evgeny, Kovba, Zarina, Nosal, Heorhii +1
#30C65 #31A15 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.01771
We study the problem of the lower bounds of the modulus of families of paths of order p, p>n-1, and their connection with the geometry of domains containing the specified families. Among other things, we have proved an analogue of Näkki's theorem on the positivity of the p-module of families of paths joining a pair of continua in the given domain. The geometry of domains with a strongly accessible boundary in the sense of the p-modulus of families of paths was also studied. We show that domains with a p-strongly accessible boundary with respect to a p-modulus, p>n-1, are are finitely connected at their boundary. The mentioned result generalizes Näkki's result, which was proved for uniform domains in the case of a conformal modulus.