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Geometry Colloquium
Seminar information archive ～04/18｜Next seminar｜Future seminars 04/19～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2015/06/12
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Kota Hattori (Keio University)
The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)
Kota Hattori (Keio University)
The nonuniqueness of tangent cone at infinity of Ricci-flat manifolds (Japanese)
[ Abstract ]
For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.
For a complete Riemannian manifold (M,g), the Gromov-Hausdorff limit of (M, r^2g) as r to 0 is called the tangent cone at infinity. By the Gromov's Compactness Theorem, there exists tangent cone at infinity for every complete Riemannian manifolds with nonnegative Ricci curvatures. Moreover, if it is Ricci-flat, with Euclidean volume growth and having at least one tangent cone at infinity with a smooth cross section, then it is uniquely determined by the result of Colding and Minicozzi. In this talk I will explain that the assumption of the volume growth is essential for their uniqueness theorem.
