Duke Mathematical Journal

Constant scalar curvature metrics with isolated singularities

Rafe Mazzeo and Frank Pacard

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 99, Number 3 (1999), 353-418.

Dates
First available: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077227909

Mathematical Reviews number (MathSciNet)
MR1712628

Zentralblatt MATH identifier
0945.53024

Digital Object Identifier
doi:10.1215/S0012-7094-99-09913-1

Subjects
Primary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 35J60: Nonlinear elliptic equations 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)

Citation

Mazzeo, Rafe; Pacard, Frank. Constant scalar curvature metrics with isolated singularities. Duke Mathematical Journal 99 (1999), no. 3, 353--418. doi:10.1215/S0012-7094-99-09913-1. http://projecteuclid.org/euclid.dmj/1077227909.


Export citation

References

  • [1] David L. Finn, Positive solutions of $\Delta\sb g u=u\sp q+Su$ singular at submanifolds with boundary, Indiana Univ. Math. J. 43 (1994), no. 4, 1359–1397.
  • [2] D. Finn, On the negative case of the singular Yamabe problem, to appear in J. Geom. Anal.
  • [3] Nicolaos Kapouleas, Complete constant mean curvature surfaces in Euclidean three-space, Ann. of Math. (2) 131 (1990), no. 2, 239–330.
  • [4] R. Kusner, R. Mazzeo, and D. Pollack, The moduli space of complete embedded constant mean curvature surfaces, Geom. Funct. Anal. 6 (1996), no. 1, 120–137.
  • [5] Rafe Mazzeo, Regularity for the singular Yamabe problem, Indiana Univ. Math. J. 40 (1991), no. 4, 1277–1299.
  • [6] Rafe Mazzeo and Frank Pacard, A construction of singular solutions for a semilinear elliptic equation using asymptotic analysis, J. Differential Geom. 44 (1996), no. 2, 331–370.
  • [7] Rafe Mazzeo, Daniel Pollack, and Karen Uhlenbeck, Connected sum constructions for constant scalar curvature metrics, Topol. Methods Nonlinear Anal. 6 (1995), no. 2, 207–233.
  • [8] Rafe Mazzeo, Daniel Pollack, and Karen Uhlenbeck, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc. 9 (1996), no. 2, 303–344.
  • [9] Rafe Mazzeo and Nathan Smale, Conformally flat metrics of constant positive scalar curvature on subdomains of the sphere, J. Differential Geom. 34 (1991), no. 3, 581–621.
  • [10] Robert C. McOwen, Singularities and the conformal scalar curvature equation, Geometric analysis and nonlinear partial differential equations (Denton, TX, 1990), Lecture Notes in Pure and Appl. Math., vol. 144, Dekker, New York, 1993, pp. 221–233.
  • [11] Frank Pacard, The Yamabe problem on subdomains of even-dimensional spheres, Topol. Methods Nonlinear Anal. 6 (1995), no. 1, 137–150.
  • [12] Richard M. Schoen, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math. 41 (1988), no. 3, 317–392.
  • [13] Richard M. Schoen, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in calculus of variations (Montecatini Terme, 1987), Lecture Notes in Math., vol. 1365, Springer, Berlin, 1989, pp. 120–154.
  • [14] R. Schoen and S.-T. Yau, Conformally flat manifolds, Kleinian groups and scalar curvature, Invent. Math. 92 (1988), no. 1, 47–71.