caa a22 4500 605515913 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0885-7 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0885-7 Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature [Elektronische Daten] [Wentao Cao, Feimin Huang, Dehua Wang] The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with large data in $${L^{\infty}}$$ L ∞ are obtained through the vanishing viscosity method and the compensated compactness framework. The $${L^{\infty}}$$ L ∞ uniform estimate and H −1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type. The global weak solutions in $${L^{\infty}}$$ L ∞ to the Gauss-Codazzi equations yield the C 1,1 isometric immersions of surfaces with the given metrics. Springer-Verlag Berlin Heidelberg, 2015 Cao Wentao Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China aut Huang Feimin Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China aut Wang Dehua Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1431-1457 0003-9527 218:3<1431 2015 218 205 https://doi.org/10.1007/s00205-015-0885-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0885-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cao Wentao Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China aut NATIONALLICENCE 700 1- Huang Feimin Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China aut NATIONALLICENCE 700 1- Wang Dehua Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1431-1457 0003-9527 218:3<1431 2015 218 205