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The structure theorems for Yetter-Drinfeld comodule algebras
Nullspaces of conformally invariant operators. Applications to $\boldsymbol{Q_k}$-curvature
1. | Department of Mathematics and Statistics, McGill University, Montréal, Canada, Canada |
2. | Department of Mathematics, University of Auckland, New Zealand &, Mathematical Sciences Institute, Australian National University, Canberra, Australia |
3. | Department of Mathematical Sciences, Seoul National University, Seoul, South Korea |
References:
[1] |
P. Baird, A. Fardoun and R. Regbaoui, Prescribed Q-curvature on manifolds of even dimension, J. Geom. Phys., 59 (2009), 221-233.
doi: 10.1016/j.geomphys.2008.10.007. |
[2] |
T. Branson and B. Ørsted, Conformal geometry and global invariants, Differential Geometry and its Applications, 1 (1991), 279-308.
doi: 10.1016/0926-2245(91)90004-S. |
[3] |
S. Brendle, Convergence of the $Q$-curvature flow on $S^4$, Adv. Math., 205 (2006), 1-32.
doi: 10.1016/j.aim.2005.07.002. |
[4] |
Y. Canzani, On the multiplicity of the eigenvalues of the conformally covariant operators, E-print, arXiv:1207.0648, July 2012. |
[5] |
Y. Canzani, A. R. Gover, D. Jakobson and R. Ponge, Conformal invariants from nodal sets. I. Negative Eigenvalues and Curvature Prescription, Int. Mat. Res. Notices, (2013).
doi: 10.1093/imrn/rns295. |
[6] |
Y. Canzani, A. R. Gover, D. Jakobson and R. Ponge, Conformal invariants II: High-dimensional nullspace,, in preparation., ().
|
[7] |
Z. Djadli and A. Malchiodi, Existence of conformal metrics with constant $Q$-curvature, Ann. of Math. (2), 168 (2008), 813-858.
doi: 10.4007/annals.2008.168.813. |
[8] |
C. L. Fefferman and C. R. Graham, $Q$-curvature and Poincaré metrics, Math. Res. Lett., 9 (2002), 139-151. |
[9] |
A. R. Gover, Q curvature prescription; forbidden functions and the GJMS null space, Proc. Amer. Math. Soc., 138 (2010), 1453-1459.
doi: 10.1090/S0002-9939-09-10111-9. |
[10] |
C. S. Gordon and E. N. Wilson, The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J., 33 (1986), 253-271.
doi: 10.1307/mmj/1029003354. |
[11] |
C. R. Graham, R. Jenne, L. J. Mason and G. A. Sparling, Conformally invariant powers of the Laplacian. I. Existence, J. Lond. Math. Soc. (2), 46 (1992), 557-565.
doi: 10.1112/jlms/s2-46.3.557. |
[12] |
C. Graham and M. Zworski, Scattering matrix in conformal geometry, Invent. Math., 152 (2003), 89-118.
doi: 10.1007/s00222-002-0268-1. |
[13] |
J. Kazdan and F. Warner, Scalar curvature and conformal deformations of Riemannian structure, J. Diff. Geom., 10 (1975), 113-134. |
[14] |
K. Kodaira and D. Spencer, On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2), 71 (1960), 43-76.
doi: 10.2307/1969879. |
[15] |
J. Lohkamp, Discontinuity of geometric expansions, Comment. Math. Helvetici, 71 (1996), 213-228.
doi: 10.1007/BF02566417. |
[16] |
T. Parker and S. Rosenberg, Invariants of conformal Laplacians, J. Differential Geom., 25 (1987), 199-222. |
[17] |
R. Ponge, Continuity and multiplicity of eigenvalues of Fredholm operators. Applications to conformally invariant operators,, in preparation., ().
|
[18] |
M. Teytel, How rare are multiple eigenvalues?, Comm. Pure Appl. Math., 52 (1999), 917-934. |
show all references
References:
[1] |
P. Baird, A. Fardoun and R. Regbaoui, Prescribed Q-curvature on manifolds of even dimension, J. Geom. Phys., 59 (2009), 221-233.
doi: 10.1016/j.geomphys.2008.10.007. |
[2] |
T. Branson and B. Ørsted, Conformal geometry and global invariants, Differential Geometry and its Applications, 1 (1991), 279-308.
doi: 10.1016/0926-2245(91)90004-S. |
[3] |
S. Brendle, Convergence of the $Q$-curvature flow on $S^4$, Adv. Math., 205 (2006), 1-32.
doi: 10.1016/j.aim.2005.07.002. |
[4] |
Y. Canzani, On the multiplicity of the eigenvalues of the conformally covariant operators, E-print, arXiv:1207.0648, July 2012. |
[5] |
Y. Canzani, A. R. Gover, D. Jakobson and R. Ponge, Conformal invariants from nodal sets. I. Negative Eigenvalues and Curvature Prescription, Int. Mat. Res. Notices, (2013).
doi: 10.1093/imrn/rns295. |
[6] |
Y. Canzani, A. R. Gover, D. Jakobson and R. Ponge, Conformal invariants II: High-dimensional nullspace,, in preparation., ().
|
[7] |
Z. Djadli and A. Malchiodi, Existence of conformal metrics with constant $Q$-curvature, Ann. of Math. (2), 168 (2008), 813-858.
doi: 10.4007/annals.2008.168.813. |
[8] |
C. L. Fefferman and C. R. Graham, $Q$-curvature and Poincaré metrics, Math. Res. Lett., 9 (2002), 139-151. |
[9] |
A. R. Gover, Q curvature prescription; forbidden functions and the GJMS null space, Proc. Amer. Math. Soc., 138 (2010), 1453-1459.
doi: 10.1090/S0002-9939-09-10111-9. |
[10] |
C. S. Gordon and E. N. Wilson, The spectrum of the Laplacian on Riemannian Heisenberg manifolds, Michigan Math. J., 33 (1986), 253-271.
doi: 10.1307/mmj/1029003354. |
[11] |
C. R. Graham, R. Jenne, L. J. Mason and G. A. Sparling, Conformally invariant powers of the Laplacian. I. Existence, J. Lond. Math. Soc. (2), 46 (1992), 557-565.
doi: 10.1112/jlms/s2-46.3.557. |
[12] |
C. Graham and M. Zworski, Scattering matrix in conformal geometry, Invent. Math., 152 (2003), 89-118.
doi: 10.1007/s00222-002-0268-1. |
[13] |
J. Kazdan and F. Warner, Scalar curvature and conformal deformations of Riemannian structure, J. Diff. Geom., 10 (1975), 113-134. |
[14] |
K. Kodaira and D. Spencer, On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2), 71 (1960), 43-76.
doi: 10.2307/1969879. |
[15] |
J. Lohkamp, Discontinuity of geometric expansions, Comment. Math. Helvetici, 71 (1996), 213-228.
doi: 10.1007/BF02566417. |
[16] |
T. Parker and S. Rosenberg, Invariants of conformal Laplacians, J. Differential Geom., 25 (1987), 199-222. |
[17] |
R. Ponge, Continuity and multiplicity of eigenvalues of Fredholm operators. Applications to conformally invariant operators,, in preparation., ().
|
[18] |
M. Teytel, How rare are multiple eigenvalues?, Comm. Pure Appl. Math., 52 (1999), 917-934. |
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