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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Covariant Riesz transform on differential forms for $p\in (1,2]$
$pin （1，2]$ 微分形式 协变里斯变换
2023/4/28
In this talk, I will introduce the recent results on $L^p$-boundedness of covariant Riesz transform on differential forms on a class of non-compact weighted Riemannian manifolds for $p\in (1,2]$ witho...
On $L^p$ inequality for differential forms and $L^p$ cohomology of a semialgebraic set for $p>>1$
differential forms semialgebraic set Geometric Topology
2011/8/23
Abstract: We study Poincar\'e type $L^p$ inequality on a compact semialgebraic subset of $\R^n$ for $p>>1$. First we derive a local inequality by using a Lipschitz deformation retraction with estimate...
A Gaussian estimate for the Heat Kernel on differential forms and application to the Riesz transform
Gaussian the Heat Kernel differential forms
2010/11/24
Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Lap...
The complete Dirichlet-to-Neumann map for differential forms
The complete Dirichlet-to-Neumann map differential forms
2010/11/11
The Dirichlet-to-Neumann map for differential forms on a Riemannian manifold with boundary is a generalization of the classical Dirichlet-to-Neumann map which arises in the problem of Electrical Imped...
Differential Forms and the Noncommutative Residue for Manifolds with Boundary II non-product metric case(to appear in Lett. Math. Phys.)(amend on 2-23-2006)
Noncommutative residue for manifolds with boundary non-product metric conformal invariant
2018/4/20
In this paper, for an even dimensional compact manifold with boundary which has the non-product metric near the boundary, we use the noncommutative residue to deˉne a conformal invariant pair. For a 4...
This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the ter...
Algebra of differential forms with exterior differential $d^3=0$ in dimension one
Algebra of differential forms exterior differential
2010/11/2
In this work, we construct the algebra of differential forms with the cube of exterior differential equal to zero on one-dimensional space. We prove that this algebra is a graded q-differential algebr...