TY - JOUR
T1 - Gromov Hyperbolicity, John Spaces, and Quasihyperbolic Geodesics
AU - Zhou, Qingshan
AU - Li, Yaxiang
AU - Rasila, Antti
N1 - Publisher Copyright:
© 2022, Mathematica Josephina, Inc.
PY - 2022/9
Y1 - 2022/9
N2 - We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a double cone arc. This result provides a new approach to an elementary metric geometry question, formulated by Heinonen (Quasiconformal mappings onto John domains. Rev Math Iberoam 5:97–123, 1989), which has been studied by Gehring et al. (Quasihyperbolic geodesics in John domains. Math Scand 36:75–92, 1989). As an application, we obtain a simple geometric condition connecting uniformity of a metric space with the existence of a Gromov hyperbolic quasihyperbolization.
AB - We show that every quasihyperbolic geodesic in a John space admitting a roughly starlike Gromov hyperbolic quasihyperbolization is a double cone arc. This result provides a new approach to an elementary metric geometry question, formulated by Heinonen (Quasiconformal mappings onto John domains. Rev Math Iberoam 5:97–123, 1989), which has been studied by Gehring et al. (Quasihyperbolic geodesics in John domains. Math Scand 36:75–92, 1989). As an application, we obtain a simple geometric condition connecting uniformity of a metric space with the existence of a Gromov hyperbolic quasihyperbolization.
KW - Gromov hyperbolic spaces
KW - John spaces
KW - Quasihyperbolic geodesic
KW - Quasihyperbolic metric
UR - http://www.scopus.com/inward/record.url?scp=85133121557&partnerID=8YFLogxK
U2 - 10.1007/s12220-022-00968-2
DO - 10.1007/s12220-022-00968-2
M3 - 文章
AN - SCOPUS:85133121557
SN - 1050-6926
VL - 32
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 9
M1 - 228
ER -