TY - JOUR

T1 - Capacity Boundary Elements in Riemannian Manifolds and Generalized Boundaries

AU - Sboev, D. A.

N1 - Supported by the Russian Science Foundation (Project 23–21–00359).

PY - 2025/6/2

Y1 - 2025/6/2

N2 - Using the capacity metric on Riemannian manifolds,we introduce capacity boundary elements and study the boundary behavior of closed mappings with bounded distortion.We establish properties of the spaces of capacity boundary elements and examine the relations between boundary elements for different exponents.The paper also examines geometric properties of a (natural) generalized boundary in domains with locally finitely connected boundary in metric spaces.It describes conditions on the metric under which the generalized boundary is unique up to homeomorphism and provides examples of such metrics in various domains.In domains with locally finitely connected boundary on Riemannian manifolds, it is shown that every element of the generalized boundary is contained in the support of some capacity boundary element.As a consequence, results on the relationship between prime ends and capacity boundary elements are obtained.

AB - Using the capacity metric on Riemannian manifolds,we introduce capacity boundary elements and study the boundary behavior of closed mappings with bounded distortion.We establish properties of the spaces of capacity boundary elements and examine the relations between boundary elements for different exponents.The paper also examines geometric properties of a (natural) generalized boundary in domains with locally finitely connected boundary in metric spaces.It describes conditions on the metric under which the generalized boundary is unique up to homeomorphism and provides examples of such metrics in various domains.In domains with locally finitely connected boundary on Riemannian manifolds, it is shown that every element of the generalized boundary is contained in the support of some capacity boundary element.As a consequence, results on the relationship between prime ends and capacity boundary elements are obtained.

KW - 517.54+517.518

KW - Mazurkiewicz metric

KW - Riemannian manifold

KW - boundary behavior

KW - capacity boundary element

KW - capacity metric

KW - closed mapping

KW - generalized boundary

KW - mapping with bounded distortion

KW - prime end

UR - https://www.mendeley.com/catalogue/8b972132-0bf4-3fd4-8048-846693a65fa2/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105007087029&origin=inward&txGid=6a0674dbb0b22a918c189412d5c89258

U2 - 10.1134/S0037446625030140

DO - 10.1134/S0037446625030140

M3 - Article

VL - 66

SP - 763

EP - 787

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -