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Search Results: 1 - 10 of 42201 matches for " Hung-Lin Chiu "
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Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants
Sagun Chanillo,Hung-Lin Chiu,Paul C. Yang
Mathematics , 2010,
Abstract: Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the non-zero eigenvalues of the Kohn Laplacian are bounded below by a positive constant provided the CR Paneitz operator is non-negative and the Webster curvature is positive. Our lower bound for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz operator and positive CR Yamabe constant are embeddable. Non-negativity of the CR Paneitz operator and positivity of the CR Yamabe constant are both CR invariant conditions and do not depend on conformal changes of the contact form. In addition we show that under the sufficient conditions above for embeddability, the embedding is stable in the sense of Burns and Epstein. We also show that for the Rossi example for non-embedability, the CR Paneitz operator is negative. For CR structures close to the standard structure on $S^3$ we show the CR Paneitz operator is positive on the space of pluriharmonic functions with respect to the standard CR structure on $S^3$.
Embedded Three Dimensional CR Manifolds and the Non-Negativity of Paneitz Operators
Sagun Chanillo,Hung-Lin Chiu,Paul Yang
Mathematics , 2012,
Abstract: Let $\Omega$ be a bounded strictly pseudoconvex domain in $C^2$ with a smooth, connected and compact boundary M and having a CR structure $J_0$ induced from $C^2$. Assume this CR structure has zero Webster torsion. Then if we deform the CR structure through real-analytic dependence on the deformation parameter and such that each deformed structure along the deformation path is smooth and embeddable in $C^2$, we show that for small deformations of the CR structure $J$ from $J_0$, the associated CR Paneitz operator for $J$ is non-negative. We also show that the Webster curvature for any ellipsoid in $C^2$ is positive. The results in this paper complement and provide partial converses to our earlier paper, (to appear Duke Math. J.) arxiv: 1007.5020.
The fundamental theorems for curves and surfaces in 3d Heisenberg group
Hung-Lin Chiu,Sin-Hua Lai
Mathematics , 2013,
Abstract: We study the local equivalence problems of curves and surfaces in three dimensional Heisenberg group via Cartans method of moving frames and Lie groups, and find a complete set of invariants for curves and surfaces. For surfaces, in terms of these invariants and their suitable derivatives, we also give a Gaussian curvature fromula of the metric induced from the adapted metric on Heisenberg group, and hence form a new formula for the Euler number of a closed surface.
Uniformization of spherical CR manifolds
Jih-Hsin Cheng,Hung-Lin Chiu,Paul Yang
Mathematics , 2013,
Abstract: Let $M$ be a closed (compact with no boundary) spherical $CR$ manifold of dimension $2n+1$. Let $\widetilde{M}$ be the universal covering of $M.$ Let $% \Phi $ denote a $CR$ developing map {equation*} \Phi :\widetilde{M}\rightarrow S^{2n+1} {equation*}% where $S^{2n+1}$ is the standard unit sphere in complex $n+1$-space $C^{n+1}$% . Suppose that the $CR$ Yamabe invariant of $M$ is positive. Then we show that $\Phi $ is injective for $n\geq 3$. In the case $n=2$, we also show that $\Phi $ is injective under the condition: $s(M)<1$. It then follows that $M$ is uniformizable.
The fundamental theorem of curves and classifications in the Heisenberg groups
Hung-Lin Chiu,XiuHong Feng,Yen-Chang Huang
Mathematics , 2015,
Abstract: We study the horizontally regular curves in the Heisenberg groups $H_n$. We show the fundamental theorem of curves in $H_n$ $(n\geq 2)$ and define the concept of the orders for horizontally regular curves. We also show that the curve $\gamma$ is of order $k$ if and only if $\gamma$ lies in $H_k$ but not in $H_{k-1}$ up to a Heisenberg rigid motion; moreover, two curves with the same order differ from a rigid motion if and only if they have the same p-curvatures and contact normality. Thus, combining with our previous work we have completed the classification of horizontally regular curves in $H_n$ for $n\geq 1$.
Monopoles and contact 3-manifolds
Jih-Hsin Cheng,Hung-Lin Chiu
Mathematics , 1999,
Abstract: We propose the study of some kind of monopole equations directly associated with a contact structure. Through a rudimentary analysis about the solutions, we show that a closed contact 3-manifold with positive Tanaka-Webster curvature and vanishing torsion must be either not symplectically semifillable or having torsion Euler class of the contact structure.
Study of P, Ca, Sr, Ba and Pb Levels in Enamel and Dentine of Human Third Molars for Environmental and Archaeological Research  [PDF]
Hwa-Yen Liu, Jiunn-Hsing Chao, Chun-Yu Chuang, Hung-Lin Chiu, Chung-Wei Yang, Yuh-Chang Sun
Advances in Anthropology (AA) , 2013, DOI: 10.4236/aa.2013.32010

Elemental determination of 80 third molars, collected from local dental clinics in Hsinchu City, Taiwan during 2009 to 2010, was conducted using inductively coupled plasma—mass spectrometry (ICP-MS). Results show that the mean concentrations of P, Ca, Sr, Ba and Pb in enamel are respectively 14.63% ± 2.19%, 27.91% ± 4.03%, 108.31 ± 35.71 ppm, 1.96 ± 1.01 ppm, and 0.72 ± 0.49 ppm. The concentrations of P, Ca and Sr are higher in enamel than in dentine, on the other hand, the concentrations of Ba and Pb are higher in dentine than in enamel. In enamel and dentine the concentrations of P, Ca and Ca/P ratio are kept constant. In enamelthe concentrations of Sr and Sr/Ca increase by age statistically but the concentrations of Ba and Ba/Ca are not. Pb concentrations in both enamel and dentine increase by age and also increase with significant differences among each birth era. This may indicate the dates of environmental exposure. The levels of Pb in this study are lower than the previous published findings before 1979. The concentrations and distribution of elements in enamel and dentine of third molars other than deciduous or permanent teeth can provide reliable base references to past and future studies.

A Fourth Order Curvature Flow on a CR 3-manifold
Shu-Cheng Chang,Jih-Hsin Cheng,Hung-Lin Chiu
Mathematics , 2005,
Abstract: Let $(\mathbf{M}^{3},J,\theta_{0})$ be a closed pseudohermitian 3-manifold. Suppose the associated torsion vanishes and the associated $Q$-curvature has no kernel part with respect to the associated Paneitz operator. On such a background pseudohermitian 3-manifold, we study the change of the contact form according to a certain version of normalized $Q$-curvature flow. This is a fourth order evolution equation. We prove that the solution exists for all time and converges smoothly to a contact form of zero $Q$ -curvature. We also consider other background conditions and obtain a priori bounds up to high orders for the solution.
The application of the moving frame method to Integral Geometry in Heisenberg group
Hung-Lin Chiu,Yen-Chang Huang,Sin-Hua Lai
Mathematics , 2015,
Abstract: We study the local equivalence problems of curves and surfaces in 3-dimensional Heisenberg group $H_1$ via Cartan's method of moving frames and Lie groups theory. We show the fundamental theorem of the curves and the surfaces in $H_1$ and find a complete set of invariants for curves and surfaces respectively. As the application of the main theorem for curves, we show Crofton's formula in terms of p-area, which makes the connection between the CR Geometry and the Integral Geometry.
Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group
Jih-Hsin Cheng,Hung-Lin Chiu,Jenn-Fang Hwang,Paul Yang
Mathematics , 2015,
Abstract: We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\geq $ $2.$ We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.
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