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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
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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
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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
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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
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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...
Noncommutative gauge theory using covariant star product defined between Lie valued differential forms
covariant star product differential forms symplectic manifold
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2010/3/18
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restric...
Casimir Effect for Differential Forms in Real Compact Hyperbolic Spaces
Casimir Effect Differential Forms Real Compact Hyperbolic Spaces
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2010/10/18
We calculate the Casimir energy associated with abelian gauge fields in real compact hyperbolic spaces. The cosmological applications of the vacuum energies are briefly considered.
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
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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...
Artinian algebras and differential forms
Artinian algebras differential forms
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2010/11/1
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
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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...