Volume 22, issue 4 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 25
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Eigenvalues of curvature, Lyapunov exponents and Harder–Narasimhan filtrations

Fei Yu

Geometry & Topology 22 (2018) 2253–2298
Bibliography
1 Y André, Slope filtrations, Confluentes Math. 1 (2009) 1 MR2571693
2 M F Atiyah, R Bott, The Yang–Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983) 523 MR702806
3 A Avila, M Viana, Simplicity of Lyapunov spectra : proof of the Zorich–Kontsevich conjecture, Acta Math. 198 (2007) 1 MR2316268
4 M Bainbridge, Euler characteristics of Teichmüller curves in genus two, Geom. Topol. 11 (2007) 1887 MR2350471
5 M Bainbridge, P Habegger, M Möller, Teichmüller curves in genus three and just likely intersections in Gmn × Gan, Publ. Math. Inst. Hautes Études Sci. 124 (2016) 1 MR3578914
6 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
7 C Bonatti, A Eskin, A Wilkinson, Projective cocycles over SL(2, ) actions : measures invariant under the upper triangular group, preprint (2017) arXiv:1709.02521
8 I I Bouw, M Möller, Teichmüller curves, triangle groups, and Lyapunov exponents, Ann. of Math. 172 (2010) 139 MR2680418
9 D Chen, M Möller, Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus, Geom. Topol. 16 (2012) 2427 MR3033521
10 D Chen, M Möller, Quadratic differentials in low genus: exceptional and non-varying strata, Ann. Sci. Éc. Norm. Supér. 47 (2014) 309 MR3215925
11 V Delecroix, P Hubert, S Lelièvre, Diffusion for the periodic wind-tree model, Ann. Sci. Éc. Norm. Supér. 47 (2014) 1085 MR3297155
12 A Eskin, M Kontsevich, M Möller, A Zorich, Lower bounds for Lyapunov exponents of flat bundles on curves, Geom. Topol. 22 (2018) 2299
13 A Eskin, M Kontsevich, A Zorich, Lyapunov spectrum of square-tiled cyclic covers, J. Mod. Dyn. 5 (2011) 319 MR2820564
14 A Eskin, M Kontsevich, A Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, Publ. Math. Inst. Hautes Études Sci. 120 (2014) 207 MR3270590
15 A Eskin, M Mirzakhani, Invariant and stationary measures for the SL(2, ) action on moduli space, preprint (2013) arXiv:1302.3320
16 A Eskin, M Mirzakhani, A Mohammadi, Isolation, equidistribution, and orbit closures for the SL(2, ) action on moduli space, Ann. of Math. 182 (2015) 673 MR3418528
17 S Filip, Semisimplicity and rigidity of the Kontsevich–Zorich cocycle, Invent. Math. 205 (2016) 617 MR3539923
18 S Filip, Splitting mixed Hodge structures over affine invariant manifolds, Ann. of Math. 183 (2016) 681 MR3450485
19 G Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. of Math. 155 (2002) 1 MR1888794
20 G Forni, C Matheus, A Zorich, Square-tiled cyclic covers, J. Mod. Dyn. 5 (2011) 285 MR2820563
21 G Forni, C Matheus, A Zorich, Lyapunov spectrum of invariant subbundles of the Hodge bundle, Ergodic Theory Dynam. Systems 34 (2014) 353 MR3233697
22 E Goujard, A criterion for being a Teichmüller curve, Math. Res. Lett. 19 (2012) 847 MR3008419
23 G Harder, M S Narasimhan, On the cohomology groups of moduli spaces of vector bundles on curves, Math. Ann. 212 (1974/75) 215 MR0364254
24 A Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954) 620 MR0063336
25 D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, E31, Vieweg (1997) MR1450870
26 J Kollár, Subadditivity of the Kodaira dimension : fibers of general type, from: "Algebraic geometry" (editor T Oda), Adv. Stud. Pure Math. 10, North-Holland, Amsterdam (1987) 361 MR946244
27 M Kontsevich, Lyapunov exponents and Hodge theory, from: "The mathematical beauty of physics" (editors J M Drouffe, J B Zuber), Adv. Ser. Math. Phys. 24, World Scientific (1997) 318 MR1490861
28 M Kontsevich, Kähler random walk and Lyapunov exponents, video-recorded lecture (2013)
29 M Kontsevich, A Zorich, Lyapunov exponents and Hodge theory, preprint (1997) arXiv:hep-th/9701164
30 M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
31 H Masur, Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982) 169 MR644018
32 H Masur, M Möller, A Zorich, Flat surfaces and dynamics on moduli space, Oberwolfach report (2014)
33 C Matheus, M Möller, J C Yoccoz, A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces, Invent. Math. 202 (2015) 333 MR3402801
34 B Mazur, Frobenius and the Hodge filtration, Bull. Amer. Math. Soc. 78 (1972) 653 MR0330169
35 B Mazur, Frobenius and the Hodge filtration (estimates), Ann. of Math. 98 (1973) 58 MR0321932
36 C T McMullen, Teichmüller curves in genus two : torsion divisors and ratios of sines, Invent. Math. 165 (2006) 651 MR2242630
37 M Möller, Variations of Hodge structures of a Teichmüller curve, J. Amer. Math. Soc. 19 (2006) 327 MR2188128
38 M Möller, Teichmüller curves, mainly from the viewpoint of algebraic geometry, from: "Moduli spaces of Riemann surfaces" (editors B Farb, R Hain, E Looijenga), IAS/Park City Math. Ser. 20, Amer. Math. Soc. (2013) 267 MR3114688
39 C T Simpson, Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988) 867 MR944577
40 W A Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. 115 (1982) 201 MR644019
41 W A Veech, Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards, Invent. Math. 97 (1989) 553 MR1005006
42 E Viehweg, K Zuo, A characterization of certain Shimura curves in the moduli stack of abelian varieties, J. Differential Geom. 66 (2004) 233 MR2106125
43 A Wright, Schwarz triangle mappings and Teichmüller curves : abelian square-tiled surfaces, J. Mod. Dyn. 6 (2012) 405 MR2988814
44 A Wright, Schwarz triangle mappings and Teichmüller curves : the Veech–Ward–Bouw–Möller curves, Geom. Funct. Anal. 23 (2013) 776 MR3053761
45 F Yu, Lyapunov exponents and Harder–Narasimhan filtrations on Teichmüller curves, conference talk (2014)
46 F Yu, K Zuo, Weierstrass filtration on Teichmüller curves and Lyapunov exponents : upper bounds, preprint (2012) arXiv:1209.2733
47 F Yu, K Zuo, Weierstrass filtration on Teichmüller curves and Lyapunov exponents, J. Mod. Dyn. 7 (2013) 209 MR3106711
48 A Zorich, Asymptotic flag of an orientable measured foliation on a surface, from: "Geometric study of foliations" (editors T Mizutani, K Masuda, S Matsumoto, T Inaba, T Tsuboi, Y Mitsumatsu), World Scientific (1994) 479 MR1363744
49 A Zorich, Finite Gauss measure on the space of interval exchange transformations : Lyapunov exponents, Ann. Inst. Fourier (Grenoble) 46 (1996) 325 MR1393518
50 A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry, I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 437 MR2261104