- Title
- Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery
- Creator
- Langford, Mat; Nguyen, Huy The
- Relation
- Calculus of Variations and Partial Differential Equations Vol. 60, Issue 6, no. 216
- Publisher Link
- http://dx.doi.org/10.1007/s00526-021-02069-4
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2021
- Description
- We study mean curvature flow in Sn/K⁺¹, the round sphere of sectional curvature K>0, under the quadratic curvature pinching condition |A|²<1/n−2H²+4K when n≥4 and |A|²<3/5H²+8/3K when n=3. This condition is related to a famous theorem of Simons (Ann Math 2(88):62–105, 1968), which states that the only minimal hypersurfaces satisfying |A|²
n or to the connected sum of a finite number of copies of S¹×Sn−1. If M is embedded, then it bounds a 1-handlebody. The results are sharp when n≥4. - Subject
- mean curvature flow; sphere; hypersurfaces; surgery
- Identifier
- http://hdl.handle.net/1959.13/1450058
- Identifier
- uon:43817
- Identifier
- ISSN:0944-2669
- Language
- eng
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