2026-09-19T12:12:36Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/322432022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Gang Tian.
Božin, Vladimir, 1973-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-03-29T18:27:09Z
2006-03-29T18:27:09Z
2004
2004
http://hdl.handle.net/1721.1/32243
56019201
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (leaves 61-64).
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.
by Vladimir Božin.
Ph.D.
64 leaves
2632174 bytes
2630560 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Geometry of Ricci-flat Kähler manifolds and some counterexamples
Thesis
application/pdf
Publication
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unknown
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