 セミナー情報
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2012年 3月12日（月）〜3月16日（金）
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| 3月13日(火) |
■幾何セミナー 15:00--16:30【会場：数学棟208】
講演者： Robert Gulliver 氏 （ミネソタ大学）
題目： Branch points of minimizing projective planes
【概要】
The variational method to find minimal surfaces in a Riemannian manifold leads to conformally parameterized surfaces with possible isolated singularities, called branch points. True branch points are those which are not a branched covering of an immersed surface. They are only possible on an area-minimizing minimal surface when the codimension is at least 2. The absence of false branch points, or more generally of ramified branch points, requires a global topological hypothesis, the Douglas hypothesis; but that has so far only been shown to suffice for orientable surfaces, and in any codimension. A branch point is ramified if in every neighborhood of the point there are two open sets which define the same piece of surface (under different parameterizations.) This talk will outline these older arguments and then discuss minimal surfaces defined on the projective plane, applying the Riemann-Hurwitz formula. We will show that in codimension one, a mapping from the projective plane which minimizes area among homotopically non-trivial mappings is an immersion.
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