Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature
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| 003 | CHVBK | ||
| 005 | 20210128100711.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0885-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0885-7 | ||
| 245 | 0 | 0 | |a Isometric Immersions of Surfaces with Two Classes of Metrics and Negative Gauss Curvature |h [Elektronische Daten] |c [Wentao Cao, Feimin Huang, Dehua Wang] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Cao |D Wentao |u Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China |4 aut | |
| 700 | 1 | |a Huang |D Feimin |u Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China |4 aut | |
| 700 | 1 | |a Wang |D Dehua |u Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1431-1457 |x 0003-9527 |q 218:3<1431 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0885-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0885-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Cao |D Wentao |u Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Huang |D Feimin |u Institute of Applied Mathematics, AMSS, CAS, 100190, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Wang |D Dehua |u Department of Mathematics, University of Pittsburgh, 15260, Pittsburgh, PA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/3(2015-12-01), 1431-1457 |x 0003-9527 |q 218:3<1431 |1 2015 |2 218 |o 205 | ||