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Teng Huang

Publications and source records attributed to Teng Huang.

46 records · Page 3Linked to original sources
arXiv2019

$L^{2}$ harmonic forms on complete special holonomy manifolds

In this article, we consider $L^{2}$ harmonic forms on a complete non-compact Riemannian manifold $X$ with a nonzero parallel form $ω$. The main result is that if $(X,ω)$ is a complete $G_{2}$- ( or $Spin(7)$-) manifold with a $d$(linear) $G_{2}$- (or $Spin(7)$-) structure form $ω$, the $L^{2}$ harmonic $2$-forms on $X$ will be vanish. As an application, we prove that the instanton equation with square integrable curvature on $(X,ω)$ only has trivial solution. We would also consider the Hodge theory on the principal $G$-bundle $E$ over $(X,ω)$.

math.DG↗
arXiv2018

Predictive and Prescriptive Analytics for Location Selection of Add-on Retail Products

In this paper, we study an analytical approach to selecting expansion locations for retailers selling add-on products whose demand is derived from the demand of another base product. Demand for the add-on product is realized only as a supplement to the demand of the base product. In our context, either of the two products could be subject to spatial autocorrelation where demand at a given location is impacted by demand at other locations. Using data from an industrial partner selling add-on products, we build predictive models for understanding the derived demand of the add-on product and establish an optimization framework for automating expansion decisions to maximize expected sales. Interestingly, spatial autocorrelation and the complexity of the predictive model impact the complexity and the structure of the prescriptive optimization model. Our results indicate that the models formulated are highly effective in predicting add-on product sales, and that using the optimization framework built on the predictive model can result in substantial increases in expected sales over baseline policies.

stat.AP↗
arXiv2017

An Energy Gap for Complex Yang-Mills Equations

We use the energy gap result of pure Yang-Mills equation [Feehan P.M.N., Adv. Math. 312 (2017), 547-587, arXiv:1502.00668] to prove another energy gap result of complex Yang-Mills equations [Gagliardo M., Uhlenbeck K., J. Fixed Point Theory Appl. 11 (2012), 185-198, arXiv:1401.7366], when Riemannian manifold $X$ of dimension $n\geq 2$ satisfies certain conditions.

math.DG↗
arXiv2017

A proof on energy gap for Yang-Mills connection

In this note, we prove an ${L^{\frac{n}{2}}}$-energy gap result for Yang-Mills connections on a principal $G$-bundle over a compact manifold without using Lojasiewicz-Simon gradient inequality (arXiv:1502.00668).

math.DG↗
arXiv2017

Stable Yang-Mills connections on Special Holonomy Manifolds

We prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact Calabi-Yau $3$-fold has holonomy equal to $SU(3)$ subject to a similar condition are holomorphic.

math.DG↗
arXiv2016

A lower bound on the solutions of Kapustin-Witten equations

In this article, we consider the Kapustin-Witten equations on a closed $4$-manifold. We study certain analytic properties of solutions to the equations on a closed manifold. The main result is that there exists an $L^{2}$-lower bound on the extra fields over a closed four-manifold satisfying certain conditions if the connections are not ASD connections. Furthermore, we also obtain a similar result about the Vafa-Witten equations.

math.DG↗
arXiv2016

Some Energy Properties of Yang-Mills Connections

We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^{n}$,$n\geq 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_{A}$ on $E$.Then we prove a mean value inequality for the density $|F_{A}|^{\frac{n}{2}}$.This inequality give rise to an energy concentrate principle for sequences of solutions that have bounded energy.We also proof that the energy must be bounded from below by some positive constant unless $E$ is a flat bundle.

math.DG↗
arXiv2016

Instantons on Cylindrical Manifolds

We consider an instanton,$\textbf{A}$,with $L^{2}$-curvature $F_{\textbf{A}}$ on the cylindrical manifold $Z=\mathbf{R}\times M$,where $M$ is a closed Riemannian $n$-manifold, $n\geq 4$.We assume $M$ admits a $3$-form $P$ and a $4$-form $Q$ satisfy $dP=4Q$ and $d\ast{Q}=(n-3)\ast P$.Manifolds with these forms include nearly Kähler 6-manifolds and nearly parallel $G_{2}$-manifolds in dimension 7.Then we can prove that the instanton must be a flat connection.

math.DG↗
arXiv2015

Yang-Mills connections on $G_{2}$-manifolds and Calabi-Yau 3-folds

We consider the minimum Yang-Mills energy on the complete $G_{2}$-manifolds and Calabi-Yau 3-folds,the connection $A$ is a stability Yang-Mills connection on the $G$-bundle $E$.We prove that the connection must be a $G_{2}$-instanton on $G_{2}$-manifold and the bundle is holomorphic on Calabi-Yau 3-fold with holonomy $SU(3)$.

math.DG↗