Mots-clés : ambient metric, Poincaré metric
@article{SIGMA_2022_18_a85,
author = {Jeffrey Case and Ayush Khaitan},
title = {The {Weighted} {Ambient} {Metric}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2022},
volume = {18},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a85/}
}
Jeffrey Case; Ayush Khaitan. The Weighted Ambient Metric. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a85/
[1] Bailey T.N., Eastwood M.G., Graham C.R., “Invariant theory for conformal and CR geometry”, Ann. of Math., 139 (1994), 491–552 | DOI | MR
[2] Bakry D., Émery M., “Diffusions hypercontractives”, Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., 1123, Springer, Berlin, 1985, 177–206 | DOI | MR
[3] Caffarelli L., Silvestre L., “An extension problem related to the fractional Laplacian”, Comm. Partial Differential Equations, 32 (2007), 1245–1260, arXiv: math.AP/0608640 | DOI | MR
[4] Case J.S., “Smooth metric measure spaces, quasi-Einstein metrics, and tractors”, Cent. Eur. J. Math., 10 (2012), 1733–1762, arXiv: 1110.3009 | DOI | MR
[5] Case J.S., “A Yamabe-type problem on smooth metric measure spaces”, J. Differential Geom., 101 (2015), 467–505, arXiv: 1306.4358 | DOI | MR
[6] Case J.S., “A notion of the weighted $\sigma_k$-curvature for manifolds with density”, Adv. Math., 295 (2016), 150–194, arXiv: 1409.4455 | DOI | MR
[7] Case J.S., “A weighted renormalized curvature for manifolds with density”, Proc. Amer. Math. Soc., 145 (2017), 4031–4040, arXiv: 1603.02989 | DOI | MR
[8] Case J.S., “The weighted $\sigma_k$-curvature of a smooth metric measure space”, Pacific J. Math., 299 (2019), 339–399, arXiv: 1608.01663 | DOI | MR
[9] Case J.S., “Sharp weighted Sobolev trace inequalities and fractional powers of the Laplacian”, J. Funct. Anal., 279 (2020), 108567, 33 pp., arXiv: 1901.09843 | DOI | MR
[10] Case J.S., Chang S.-Y.A., “On fractional GJMS operators”, Comm. Pure Appl. Math., 69 (2016), 1017–1061, arXiv: 1406.1846 | DOI | MR
[11] Case J.S., Shu Y.-J., Wei G., “Rigidity of quasi-Einstein metrics”, Differential Geom. Appl., 29 (2011), 93–100, arXiv: 0805.3132 | DOI | MR
[12] Chang S.-Y.A., Fang H., “A class of variational functionals in conformal geometry”, Int. Math. Res. Not., 2008, 2008, rnn008, 16 pp., arXiv: 0803.0333 | DOI | MR
[13] Chang S.-Y.A., Fang H., Graham C.R., “A note on renormalized volume functionals”, Differential Geom. Appl., 33, suppl. (2014), 246–258, arXiv: 1211.6422 | DOI | MR
[14] Cheeger J., Colding T.H., “On the structure of spaces with Ricci curvature bounded below. II”, J. Differential Geom., 54 (2000), 13–35, arXiv: 1805.07988 | DOI | MR
[15] Fefferman C., Graham C.R., The ambient metric, Ann. of Math. Stud., 178, Princeton University Press, Princeton, NJ, 2012 | MR
[16] Gover A.R., “Invariant theory and calculus for conformal geometries”, Adv. Math., 163 (2001), 206–257 | DOI | MR
[17] Gover A.R., Leitner F., “A sub-product construction of Poincaré–Einstein metrics”, Internat. J. Math., 20 (2009), 1263–1287, arXiv: math.DG/0608044 | DOI | MR
[18] Graham C.R., “Extended obstruction tensors and renormalized volume coefficients”, Adv. Math., 220 (2009), 1956–1985, arXiv: 0810.4203 | DOI | MR
[19] Graham C.R., Jenne R., Mason L.J., Sparling G.A.J., “Conformally invariant powers of the Laplacian. I Existence”, J. London Math. Soc., 46 (1992), 557–565 | DOI | MR
[20] Graham C.R., Zworski M., “Scattering matrix in conformal geometry”, Invent. Math., 152 (2003), 89–118, arXiv: math.DG/0109089 | DOI | MR
[21] Khaitan A., GJMS operators on smooth metric measure spaces, arXiv: 2203.04719
[22] Mazzeo R.R., Melrose R.B., “Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature”, J. Funct. Anal., 75 (1987), 260–310 | DOI | MR
[23] Perelman G., The entropy formula for the {R}icci flow and its geometric applications, arXiv: math.DG/0211159
[24] Wei G., Wylie W., “Comparison geometry for the Bakry–Emery Ricci tensor”, J. Differential Geom., 83 (2009), 377–405, arXiv: 0706.1120 | DOI | MR
[25] Yamabe H., “On a deformation of Riemannian structures on compact manifolds”, Osaka Math. J., 12 (1960), 21–37 | MR