An integral equation in conformal geometry

Fengbo Hang; Xiaodong Wang; Xiaodong Yan

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 1, page 1-21
  • ISSN: 0294-1449

How to cite

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Hang, Fengbo, Wang, Xiaodong, and Yan, Xiaodong. "An integral equation in conformal geometry." Annales de l'I.H.P. Analyse non linéaire 26.1 (2009): 1-21. <http://eudml.org/doc/78836>.

@article{Hang2009,
author = {Hang, Fengbo, Wang, Xiaodong, Yan, Xiaodong},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {isoperimetric inequalities; Poisson kernel; Yamabe type integral equations},
language = {eng},
number = {1},
pages = {1-21},
publisher = {Elsevier},
title = {An integral equation in conformal geometry},
url = {http://eudml.org/doc/78836},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Hang, Fengbo
AU - Wang, Xiaodong
AU - Yan, Xiaodong
TI - An integral equation in conformal geometry
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 1
SP - 1
EP - 21
LA - eng
KW - isoperimetric inequalities; Poisson kernel; Yamabe type integral equations
UR - http://eudml.org/doc/78836
ER -

References

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  1. [1] Adams R.A., Sobolev Spaces, Pure and Applied Mathematics, vol. 65, second ed., Academic Press, New York–London, 2003. Zbl0314.46030MR450957
  2. [2] Baernstein A., Taylor B.A., Spherical rearrangements, sub-harmonic functions and *-functions in n-space, Duke Math. J.43 (1976) 245-268. Zbl0331.31002MR402083
  3. [3] Carleman T., Zur Theorie der Minimalflächen, Math. Z.9 (1921) 154-160. Zbl48.0590.02MR1544458JFM48.0590.02
  4. [4] Escobar J.F., The Yamabe problem on manifolds with boundary, J. Differential Geom.35 (1) (1992) 21-84. Zbl0771.53017MR1152225
  5. [5] Escobar J.F., Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary, Ann. of Math. (2)136 (1) (1992) 1-50. Zbl0766.53033MR1173925
  6. [6] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, second ed., third printing, Springer-Verlag, Berlin, 1998. Zbl0562.35001
  7. [7] F.B. Hang, X.D. Wang, X.D. Yan, Sharp integral inequalities for harmonic functions, Comm. Pure Appl. Math., in press. Zbl1173.26321
  8. [8] S. Jacobs, An isoperimetric inequality for functions analytic in multiply connected domains, Mittag-Leffler Institute report, 1972. 
  9. [9] Lee J.M., Parker T.H., The Yamabe problem, Bull. Amer. Math. Soc. (N.S.)17 (1) (1987) 37-91. Zbl0633.53062MR888880
  10. [10] Lions P.L., The concentration-compactness principle in the calculus of variations. The limit case. II, Rev. Mat. Iberoamericana1 (2) (1985) 45-121. Zbl0704.49006MR850686
  11. [11] Stein E.M., Weiss G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton Mathematical Series, vol. 32, Princeton University Press, Princeton, NJ, 1971. Zbl0232.42007MR304972

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