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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Lines on holomorphic contact manifolds and a generalization of (2,3,5)-distributions to higher dimensions
全纯接触流形 线和 （2，3，5） 高维度推广
2023/4/19
Since the celebrated work by Cartan, distributions with small growth vector (2,3,5) have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic (2,...
Let A(t) denote the cluster produced by internal diffusion limited aggregation (internal DLA) with t particles in dimension d ≥ 3. We show that A(t) is approximately spherical, up to an O(√log t) erro...
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...
Let A(t) denote the cluster produced by internal di usion limited aggregation (internal DLA) with t particles in dimension d 3. We show that A(t) is approximately spherical, up to an O(
p log t) er...
Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of...
Closed nodal surfaces for simply connected domains in higher dimensions
Laplacian eigenfunction nodal domain
2010/12/1
We give an example of a domain in dimension N 3, homeomorphic to a ball and with analytic boundary, for which the second eigenvalue of the Dirichlet Laplacian has an eigenfunction with a closed noda...
Global existence of the heat flow for H-systems in higher dimensions
Global existence heat flow H-systems higher dimensions
2018/4/20
In this paper we consider the heat flow for the H-system with variable function H (·) in higher dimensions, and establish global existence and uniqueness.