4 papers · 1 filter
Alexandrov--Fenchel inequalities for closed axisymmetric hypersurfaces
Weimin Sheng, Yinhang Wang
We establish sharp Alexandrov--Fenchel inequalities for closed, embedded, axisymmetric hypersurfaces Sigma in n+1 dimensional Euclidean space R^{n+1}, the dimension n > or = 2, wit…
Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let k be an integer from 1 to n, let f be a positive smooth function on the unit sphere, and consider the normalized flow X_t = -f({nu})|X|^{alpha} sigma_k({kappa}) {nu} + beta X,…
Non-homogeneous curvature flows in a hemisphere
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let S^{n+1}_{+} be the open hemisphere of the unit sphere S^{n+1} centred at o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^{alpha} {nu} of smooth, closed, strict…
Non-homogeneous curvature flows in hyperbolic space
Hongyi Sheng, Weimin Sheng, Jiazhuo Yang
Let H^{n+1} be hyperbolic space of sectional curvature -1, with a fixed point o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^{alpha} {nu} of smooth, closed, stric…