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Geometry of Ricci-flat Kähler manifolds and some counterexamples

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dc.contributor.advisor Gang Tian. en_US Božin, Vladimir, 1973- en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2006-03-29T18:27:09Z 2006-03-29T18:27:09Z 2004 en_US 2004 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004. en_US
dc.description Includes bibliographical references (leaves 61-64). en_US
dc.description.abstract In this work, we study geometry of Ricci-flat Kähler manifolds, and also provide some counterexample constructions. We study asymptotic behavior of complete Ricci-flat metrics at infinity and consider a construction of approximate Ricci-flat metrics on quasiprojective manifolds with a divisor with normal crossings removed, by means of reducing torsion of a non-Kähler metric with the right volume form. Next, we study special Lagrangian fibrations using methods of geometric function theory. In particular, we generalize the method of extremal length and prove a generaliziation of the Teichmiiller theorem. We relate extremal problems to the existence of special Lagrangian fibrations in the large complex structure limit of Calabi-Yau manifolds. We proceed to some problems in the theory of minimal surfaces, disproving the Schoen-Yau conjecture and providing a first example of a proper harmonic map from the unit disk to a complex plane. In the end, we prove that the union closed set conjecture is equivalent to a strengthened version, giving a construction which might lead to a counterexample. en_US
dc.description.statementofresponsibility by Vladimir Božin. en_US
dc.format.extent 64 leaves en_US
dc.format.extent 2632174 bytes
dc.format.extent 2630560 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.subject Mathematics. en_US
dc.title Geometry of Ricci-flat Kähler manifolds and some counterexamples en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 56019201 en_US

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