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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A simpler proof of the Frank-Lieb inequality on the Heisenberg group
海森堡群 Frank-Lieb inequality 更简单证明
2023/4/14
I will discuss the Hardy-Littlewood integral inequality with sharp constant on the Heisenberg goup proved by Frank and Lieb. I will outline a simpler proof which bypasses the sophisticated argument fo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlocal Filtration Equations on the Heisenberg group
海森堡群 非局部 滤波方程
2023/4/28
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Nonlocal Filtration Equations on the Heisenberg group
海森堡群 非局部 滤波方程
2023/5/4
Since the work by Caffarelli-Chan-Silvestre-Vasseur, integro-differential equations naturally arise from models in physics, engineering, and finance, attracting an increasing level of interest. They a...
CUP PRODUCTS, THE HEISENBERG GROUP, AND CODIMENSION TWO ALGEBRAIC CYCLES
CUP PRODUCTS HEISENBERG GROUP
2015/12/10
We de ne higher categorical invariants (gerbes) of codimension two algebraic cycles and provide
a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This...
Some properties of Holder surfaces in the Heisenberg group
properties of Holder surfaces Heisenberg group Differential Geometry
2012/5/9
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into ...
Banach Gabor frames with Hermite functions: polyanalytic spaces from the Heisenberg group
Gabor frames Heisenberg group Hermite functions
2011/2/23
Gabor frames with Hermite functions are equivalent to sampling sequences in true Fock spaces of polyanalytic functions. In the L2-case, such an equivalence follows from the unitarity of the polyanalyt...
On fully nonlinear CR invariant equations on the Heisenberg group
nonlinear CR invariant equations Heisenberg group
2010/11/8
In this paper we provide a characterization of second order fully nonlinear CR invariant equations on the Heisenberg group, which is the analogue in the CR setting of the result proved in the Euclide...
The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group
Yamabe equation quaternionic contact structures
2010/12/7
We determine the best (optimal) constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group and the non-negative functions for which equality holds.
Sharp constants in several inequalities on the Heisenberg group
Sharp constants in several inequalities Heisenberg group
2010/12/1
We derive the sharp constants for the inequalities on the Heisenberg group Hn whose analogues on Euclidean space Rn are the well known Hardy-Littlewood- Sobolev inequalities. Only one special case had...
Intersections of intrinsic submanifolds in the Heisenberg group
Heisenberg group intrinsic regular surfaces implicit function theorem
2010/12/14
In the first Heisenberg group, we show that the intersection of two intrinsic submanifolds with linearly independent horizontal normals locally coincides with the image of an injective continuous curv...
Poincare Inequalities for the Heisenberg Group Target
Heisenberg group Sobolev space Poincare type inequality
2008/6/27
In this paper some Poincare type inequalities are obtained for the maps of the Heisenberg group target.
Some Hardy Type Inequalities in the Heisenberg Group
Hardy inequality Picone identity Heisenberg group
2008/6/27
Some Hardy type inequalities on the domain in the Heisenberg group are established by using the Picone type identity and constructing suitable auxiliary functions.
Global Poincar′e inequalities on the Heisenberg group and applications
Heisenberg group Sobolev inequalities Poincar\'e inequalities best constants
2007/12/11
Let $f$ be in the localized nonisotropic Sobolev space $W_{\rm loc}^{1,p}(\Bbb H^n) $ on the $n$-dimensional Heisenberg group $\Bbb H^n=\Bbb C^n\times \Bbb R$, where $1\leq p is the h...
A Borsuk-Ulak Theorem for Heisenberg Group Actions
Borsuk-Ulam Type Theorem Cohomological Index Group Action
2010/3/1
Let G=H2n+1 be a (2n+1)-dimensional Heisenberg Lie group acts on M=Cm-\{0\} and M'=Cm'-\{0\} exponentially. By using Cohomological Index we proved the following theorem. If f:M{\to}M' is a G-equivaria...