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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures
正交投影 混合范数 度量维度 分析插值
2023/5/5
We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
Neighborliness of Randomly-Projected Simplices in High Dimensions
Neighborly Polytopes Convex Hull of Gaussian Sample
2015/8/21
Let A be a d by n matrix, d < n. Let T = T
n−1 be the standard regular simplex in R
n
.
We count the faces of the projected simplex AT in the case where the projection is random,
the dimens...
The complex Goldberg-Sachs theorem in higher dimensions
The complex Goldberg-Sachs theorem higher dimensions Differential Geometry
2011/9/2
Abstract: We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+\epsilon)$-dimensional complex Riemannian manifold $(\mathcal{M}, \bm{g})$, where $\epsilo...
Global well-posedness and scattering for the defocusing cubic NLS in four dimensions
Global well-posedness scattering the defocusing cubic NLS
2010/11/11
In this short note we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical NLS in four space dimensions obtained previously by Ryckman and Visan. ...
Finsler connection preserving angle in dimensions $N\ge3$
Finsler connection preserving dimensions $N\ge3$
2010/12/1
We show that if a Finsler space is conformally automorphic to a Riemannian space and the automorphism is positively homogeneous with respect to tangent vectors, then the indicatrix of the Finsler spac...
<正> In a recent paper of the same title we studied the plane sectionsof the circumscribed developable of a curve in the projective n-dimen-sional space Sn(n(?)3) confining ourselves to the considerati...
<正> In the present paper we propose to establish certain theoremsconcerning plane sections of the circumscribed developable of a curvein the projective n-dimensional space s_n((?)3).The planes in cons...