A unified flow approach to smooth, even Lp-Minkowski problems

By Paul Bryan, Mohammad N. Ivaki, Julian Scheuer. Analysis & PDE, 2016

69 citations recorded by the source corpus.

We study long-time existence and asymptotic behaviour for a class of anisotropic, expanding curvature flows. For this we adapt new curvature estimates, which were developed by Guan, Ren and Wang to treat some stationary prescribed curvature problems. As an application we give a unified flow approach to the existence of smooth, even $L_p$-Minkowski problems in $\mathbb{R}^{n+1}$ for $p>-n-1.$

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/c017ce15a89c1df83caaa68f5dcbc5fea28ae1fc

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In Applied Mathematics

1. Changyu Ren
2. Zhizhang Wang
3. Duong H. Phong
4. Sebastien Picard
5. Xiangwen Zhang

Citations in the corpus

• The global curvature estimate for the n-2 Hessian equation (2020, methodology): “Our estimate established in [26] is also applied by Xiao [50] and Bryan-Ivaki-Scheuer [10] respectively in some geometric flow problems.”