Compactness of conformal metrics with positive gaussian curvature in ℝ 2

Kuo-Shung Cheng; Chang-Shou Lin

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 1, page 31-45
  • ISSN: 0391-173X

How to cite

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Cheng, Kuo-Shung, and Lin, Chang-Shou. "Compactness of conformal metrics with positive gaussian curvature in $\mathbb {R}^2$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.1 (1998): 31-45. <http://eudml.org/doc/84322>.

@article{Cheng1998,
author = {Cheng, Kuo-Shung, Lin, Chang-Shou},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {elliptic equation; entire solution; compactness},
language = {eng},
number = {1},
pages = {31-45},
publisher = {Scuola normale superiore},
title = {Compactness of conformal metrics with positive gaussian curvature in $\mathbb \{R\}^2$},
url = {http://eudml.org/doc/84322},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Cheng, Kuo-Shung
AU - Lin, Chang-Shou
TI - Compactness of conformal metrics with positive gaussian curvature in $\mathbb {R}^2$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 1
SP - 31
EP - 45
LA - eng
KW - elliptic equation; entire solution; compactness
UR - http://eudml.org/doc/84322
ER -

References

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  1. [A] P. Aviles, Conformal complete metrics with prescribed non-negative Gaussian curvature in R2, Invent. Math.83 (1986), 519-544. Zbl0592.53034MR827365
  2. [BM] H. Brezis - F. Merle, Estimates on the solutions of Δu = v (x) exp u (x) on R2, Comm. Partial Differential Equations16 (1991), 1223-1253. Zbl0746.35006
  3. [CL] W.-X. Cheng - C.-M. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J.63 (1991), 615-622. Zbl0768.35025MR1121147
  4. [CLn] K.-S. Cheng - C.-S. Lin, On the asymptotic behavior of solutions of the conformal Gaussian curvature equation in R2, Math. Ann.308 (1991), 119-139 Zbl0871.35014MR1446203
  5. [CN1] K.-S. Cheng - W.-M. Ni, On the structure of the conformal Gaussian curvature equation on R2 I., Duke. Math. J.62 (1991), 721-737. Zbl0733.35037MR1104815
  6. [CN2] K.-S. Cheng - W.-M. Ni, On the structure of the conformal Gaussian curvature equation on R2 II, Math. Ann.290 (1991), 671-680. Zbl0753.35032MR1119945
  7. [CY1] S.Y.A. Chang - P.C. Yang, Prescribing Gaussian curvature on S2, Acta Math.159 (1987), 215-259. Zbl0636.53053MR908146
  8. [CY2] S.Y.A. Chang - P.C. Yang, Conformal deformation of metric on S2, J. Differential Geom.27 (1988), 259-296. Zbl0649.53022MR925123
  9. [H] Z.-C. Han, Prescribing Gaussian curvature on S2, Duke Math. J.61 (1990), 679-703. Zbl0715.53034MR1084455
  10. [M] R. McOwen, Conformal metric in R2 with prescribed Gaussian curvature and positive total curvature, Indiana Univ. Math. J.34 (1985), 97-104. Zbl0546.53032MR773395

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