School of Mathematical Sciences
https://qmro.qmul.ac.uk/xmlui/handle/123456789/3478
2022-05-26T02:05:56ZAddressing the socioeconomic divide in computational modeling for infectious diseases
https://qmro.qmul.ac.uk/xmlui/handle/123456789/78558
Addressing the socioeconomic divide in computational modeling for infectious diseases
Perra, N; Tizzoni, M; Nsoesie, E; Gauvin, L; Karsai, M; Bansal, S
2022-05-24T00:00:00ZComplex systems: the amazing cross-disciplinary journey of statistical physics
https://qmro.qmul.ac.uk/xmlui/handle/123456789/78539
Complex systems: the amazing cross-disciplinary journey of statistical physics
Beck, C
2022-02-28T00:00:00ZComplexity and Persistence of Price Time Series of the European Electricity Spot Market
https://qmro.qmul.ac.uk/xmlui/handle/123456789/78538
Complexity and Persistence of Price Time Series of the European Electricity Spot Market
Han, C; Hilger, H; Mix, E; Böttcher, PC; Reyers, M; Beck, C; Witthaut, D; Gorjão, LR
2022-04-07T00:00:00ZQuadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery
https://qmro.qmul.ac.uk/xmlui/handle/123456789/78521
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery
Langford, M; Nguyen, HT
We study mean curvature flow in SKn+1, the round sphere of sectional curvature K> 0 , under the quadratic curvature pinching condition |A|2<1n-2H2+4K when n≥ 4 and |A|2<35H2+83K 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< nK are the totally geodesic hyperspheres. It is related to but distinct from “two-convexity”. Notably, in contrast to two-convexity, it allows the mean curvature to change sign. We show that the pinching condition is preserved by mean curvature flow, and obtain a “cylindrical” estimate and corresponding pointwise derivative estimates for the curvature. As a result, we find that the flow becomes either uniformly convex or quantitatively cylindrical in regions of high curvature. This allows us to apply the surgery apparatus developed by Huisken and Sinestrari (Invent Math 175(1):137–221, 2009) (cf. Haslhofer and Kleiner, Duke Math J 166(9):1591–1626, 2017). We conclude that any smoothly, properly immersed hypersurface M of SKn+1 satisfying the pinching condition is diffeomorphic to Sn 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.
2021-12-01T00:00:00Z