@incollection{AST_2008__321__31_0, author = {Liu, Kefeng and Sun, Xiaofeng and Yau, Shing-Tung}, title = {Geometry of moduli spaces}, booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (I) : Volume en l'honneur de Jean Pierre Bourguignon}, editor = {Hijazi Oussama}, series = {Ast\'erisque}, pages = {31--50}, publisher = {Soci\'et\'e math\'ematique de France}, number = {321}, year = {2008}, mrnumber = {2521643}, zbl = {1183.53069}, language = {en}, url = {http://archive.numdam.org/item/AST_2008__321__31_0/} }
TY - CHAP AU - Liu, Kefeng AU - Sun, Xiaofeng AU - Yau, Shing-Tung TI - Geometry of moduli spaces BT - Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon AU - Collectif ED - Hijazi Oussama T3 - Astérisque PY - 2008 SP - 31 EP - 50 IS - 321 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2008__321__31_0/ LA - en ID - AST_2008__321__31_0 ER -
%0 Book Section %A Liu, Kefeng %A Sun, Xiaofeng %A Yau, Shing-Tung %T Geometry of moduli spaces %B Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon %A Collectif %E Hijazi Oussama %S Astérisque %D 2008 %P 31-50 %N 321 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2008__321__31_0/ %G en %F AST_2008__321__31_0
Liu, Kefeng; Sun, Xiaofeng; Yau, Shing-Tung. Geometry of moduli spaces, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 31-50. http://archive.numdam.org/item/AST_2008__321__31_0/
[1] Riemann's mapping theorem for variable metrics", Ann. of Math. 72 (1960), p. 385-404. | DOI | MR | Zbl
& - "[2] On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of Fefferman's equation", Comm. Pure Appl. Math. 33 (1980), p. 507-544. | DOI | MR | Zbl
& - "[3] The irreducibility of the space of curves of given genus", Publ. Math. I.H.É.S. 36 (1969), p. 75-109. | DOI | EuDML | Numdam | MR | Zbl
& - "[4] Collars on Riemann surfaces", in Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973), Princeton Univ. Press, 1974, p. 263-268. Ann. of Math. Studies, No. 79. | MR | Zbl
- "[5] Canonical metrics on the moduli space of Riemann surfaces. I", J. Differential Geom. 68 (2004), p. 571-637. | DOI | MR | Zbl
, & - "[6] Canonical metrics on the moduli space of Riemann surfaces. II", J. Differential Geom. 69 (2005), p. 163-216. | DOI | MR | Zbl
, & , "[7] Good metrics on the moduli space of Riemann surface I", preprint, 2008.
, & , "[8] Good metrics on the moduli space of Riemann surface II", preprint, 2008.
, & , "[9] On the Weil-Petersson volume and the first Chern class of the moduli spaces of Calabi -Yau manifolds", submitted to Communications in Mathematical Physics. | MR | Zbl
& - "[10] The moduli space of Riemann surfaces is Kähler hyperbolic", Ann. of Math. 151 (2000), p. 327-357. | DOI | EuDML | MR | Zbl
- "[11] Hirzebruch's proportionality theorem in the noncompact case", Invent. Math. 42 (1977), p. 239-272. | DOI | EuDML | MR | Zbl
- "[12] Harmonic maps of the moduli space of compact Riemann surfaces", Math. Ann. 275 (1986), p. 455-466. | DOI | EuDML | MR | Zbl
- "[13] The curvature of the Petersson-Weil metric on the moduli space of Kähler-Einstein manifolds", in Complex analysis and geometry, Univ. Ser. Math., Plenum, 1993, p. 339-354. | DOI | MR | Zbl
, "[14] Curvature of the Weil-Petersson metric in the moduli space of compact Kahler-Einstein manifolds of negative first Chern class", in Contributions to several complex variables, Aspects Math., E9, Vieweg, 1986, p. 261-298. | DOI | MR | Zbl
- "[15] On the determinant of the bundle of meromorphic quadratic differentials on the Deligne-Mumford compactification of the moduli space of Riemann surfaces", Math. Ann. 293 (1992), p. 681-705. | DOI | EuDML | MR | Zbl
- "[16] Chern forms and the Riemann tensor for the moduli space of curves", Invent Math. 85 (1986), p. 119-145. | DOI | EuDML | MR | Zbl
- "[17] Asymptotics of the spectrum and the Selberg zeta function on the space of Riemann surfaces", Comm. Math. Phys. 112 (1987), p. 283-315. | DOI | MR | Zbl
, "[18] The hyperbolic metric and the geometry of the universal curve", J. Differential Geom. 31 (1990), p. 417-472. | DOI | MR | Zbl
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