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We construct large families of new collapsing hyperk\"ahler metrics on the K3 surface.
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1984
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E. Luft and D. Sjerve, 3 3 -manifolds with subgroups 𝐙 ⊕ 𝐙 ⊕ 𝐙 {\bf Z}\oplus{\bf Z}\oplus{\bf Z} in their fundamental groups , Pacific J. Math. 114
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by same author, The L 2 L^{2} structure of moduli spaces of Einstein metrics on 4 4 -manifolds , Geom. Funct. Anal. 2
1992
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A. S. Dancer, Nahm’s equations and hyper-Kähler geometry , Comm. Math. Phys. 158
1993
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M. Micallef and J. Wolfson, The second variation of area of minimal surfaces in four-manifolds , Math. Ann. 295
1993
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S.-T. Yau, Open problems in geometry , Differential geometry: partial differential equations on manifolds (Los Angeles, CA, 1990), Proc. Sympos. Pure Math., vol. 54, Amer. Math. Soc., Providence, RI, 1993, pp. 1–28
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J. M. Figueroa-O’Farrill, C. Köhl, and B. Spence, Supersymmetric Yang-Mills, octonionic instantons and triholomorphic curves , Nuclear Phys. B 521
1998
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by same author, Area minimizers in a K 3 K3 surface and holomorphicity , Geom. Funct. Anal. 16
2006
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S. Hohloch, G. Noetzel, and D. A. Salamon, Hypercontact structures and Floer homology , Geom. Topol. 13
2009
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V. Minerbe, A mass for ALF manifolds , Comm. Math. Phys. 289
2009
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by same author, A survey of Einstein metrics on 4-manifolds , Handbook of geometric analysis, No. 3, Adv. Lect. Math. (ALM), vol. 14, Int. Press, Somerville, MA, 2010, pp. 1–39
2010
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by same author, On the asymptotic geometry of gravitational instantons , Ann. Sci. Éc. Norm. Supér. (4) 43
2010
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S. A. Cherkis and A. Kapustin, Singular monopoles and gravitational instantons , Comm. Math. Phys. 203
1999
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C. Arezzo and M. J. Micallef, Minimal surfaces in flat tori , Geom. Funct. Anal. 10
2000
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M. Gross and P. M. H. Wilson, Large complex structure limits of K 3 K3 surfaces , J. Differential Geom. 55
2000
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by same author, L 2 L^{2} -cohomology of hyperkähler quotients , Comm. Math. Phys. 211
2000
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J. Lott, Collapsing and Dirac-type operators , Proceedings of the Euroconference on Partial Differential Equations and their Applications to Geometry and Physics (Castelvecchio Pascoli, 2000), vol. 91, 2002, pp. 175–196
2002
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by same author, Collapsing and the differential form Laplacian: the case of a smooth limit space , Duke Math. J. 114
2002
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G. Tian, Some regularity problems of stationary harmonic maps , Noncompact problems at the intersection of geometry, analysis, and topology, Contemp. Math., vol. 350, Amer. Math. Soc., Providence, RI, 2004, pp. 245–252
2004
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2011
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B. Charbonneau and J. Hurtubise, Singular Hermitian-Einstein monopoles on the product of a circle and a Riemann surface , Int. Math. Res. Not. (2011), no. 1, 175–216
2011
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S. Donaldson and E. Segal, Gauge theory in higher dimensions, II , Surveys in differential geometry. Volume XVI. Geometry of special holonomy and related topics, Surv. Differ. Geom., vol. 16, Int. Press, Somerville, MA, 2011, pp. 1–41
2011
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by same author, Rigidity for multi-Taub-NUT metrics , J. Reine Angew. Math. 656
2011
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J. A. Wolf, Spaces of constant curvature , sixth ed., AMS Chelsea Publishing, Providence, RI, 2011
2011
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H. Auvray, From ALE to ALF gravitational instantons , 2012, arXiv:1210.1654
2012
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by same author, Calabi-Yau metrics on Kummer surfaces as a model gluing problem , Advances in geometric analysis, Adv. Lect. Math. (ALM), vol. 21, Int. Press, Somerville, MA, 2012, pp. 109–118
2012
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H.-J. Hein, Gravitational instantons from rational elliptic surfaces , J. Amer. Math. Soc. 25
2012
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by same author, From ALE to ALF gravitational instantons. II , 2013, arXiv:1304.3342
2013
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C. Bellettini and G. Tian, Compactness results for triholomorphic maps , 2015, arXiv:1507.06558
2015
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2015
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