Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery

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|²n 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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