Short loops in surfaces with a circular boundary component
It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing that if S is a Riemannian surface with connected boundary in Rn, such that the boundary curve is a standard unit circle, t...
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| Format: | Journal article |
| Język: | English |
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World Scientific Publishing
2018
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| Streszczenie: | It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing that if S is a Riemannian surface with connected boundary in Rn, such that the boundary curve is a standard unit circle, then the length of the shortest non-contractible loop in S is bounded in terms of the area of S. |
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