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Akademický článek

Autor: Xi Dongmeng, Yang Deane, Zhang Gaoyong, Zhao Yiming

Publikováno v: Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 907-945 (2023)

Chord measures are newly discovered translation-invariant geometric measures of convex bodies in Rn{{\mathbb{R}}}^{n}, in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random

Externí odkaz: https://doaj.org/article/0fc176d040524ede90edd5979b7dc829

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The $L_p$-Minkowski problem for $-n < p< 1$

Autor: Bianchi, Gabriele, Böröczky, Károly J., Colesanti, Andrea, Yang, Deane

Publikováno v: Advances in Mathematics 341 (2019), pp. 493-535

Chou and Wang's existence result for the $L_p$-Minkowski problem on ${\mathbb S}^{n-1}$ for $p\in(-n,1)$ and an absolutely continuous measure $\mu$ is discussed and extended to more general measures. In particular, we provide an almost optimal suffic

Externí odkaz: http://arxiv.org/abs/1710.04401

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The dual Minkowski problem for symmetric convex bodies

Autor: Böröczky, Károly, Lutwak, Erwin, Yang, Deane, Zhang, Gaoyong, Zhao, Yiming

The dual Minkowski problem for even data asks what are the necessary and sufficient conditions on an even prescribed measure on the unit sphere for it to be the $q$-th dual curvature measure of an origin-symmetric convex body in $\mathbb{R}^n$. A ful

Externí odkaz: http://arxiv.org/abs/1703.06259

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Isometric embedding via strongly symmetric positive systems

Autor: Chen, Gui-Qiang, Clelland, Jeanne, Slemrod, Marshall, Wang, Dehua, Yang, Deane

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated arguments vi

Externí odkaz: http://arxiv.org/abs/1502.04356

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