论文标题
在指数的杨米尔斯和$ P $ -YANG-MILLS FIELDS上
On exponential Yang-Mills fields and $p$-Yang-Mills fields
论文作者
论文摘要
我们介绍\ emph {归一化的Yang-mills Energy函数} $ \ MATHCAL {ym} _e^0 $，压力 - 增强量张量$ s_ {e，\ Mathcal {ym}^0} $ e $ - 保护法。我们还介绍了{\ it $ e $ -degree} $ d_e $的概念，该$在关联中连接两个单独的部分，将指数的压力 - 能量能量张紧$ s_ {对于指数杨米尔斯字段。这些单调性公式和消失的定理用于指数阳米尔斯字段增强并扩展了单调性公式，并在[DW]和[W11，9.2]中以$ f $ -YANG-MILLS FIELDS的$ f $ -YANG-MILLS FIELDS进行消失。我们还讨论了平均原则（参见命题8.1），等静脉和索波列夫，不平等，凸态和詹森的不平等，$ p $ -yang-mills田野，一种局外的平均变异方法，用于变化的计算中（参见[w1，w3]）和$φ_ $ cou _ ^（3）;观点和观点（参见定理6.1、7.1、9.1、9.2、10.1,10.2、11.13、11.14、11.15））。
We introduce \emph{normalized exponential Yang-Mills energy functional} $\mathcal{YM}_e^0$, stress-energy tensor $S_{e,\mathcal{YM}^0 }$ associated with the normalized \emph{exponential Yang-Mills energy functional} $\mathcal{YM}_e ^0 $, $e$-conservation law. We also introduce the notion of the {\it $e$-degree} $d_e$ which connects two separate parts in the associated normalize exponential stress-energy tensor $S_{e,\mathcal{YM}^0 }$ (cf. (3.10) and (4.15)), derive monotonicity formula for exponential Yang-Mills fields, and prove a vanishing theorem for exponential Yang-Mills fields. These monotonicity formula and vanishing theorem for exponential Yang-Mills fields augment and extend monotonicity formula and vanishing theorem for $F$-Yang-Mills fields in [DW] and [W11, 9.2]. We also discuss an average principle (cf. Proposition 8.1), isoperimetric and Sobolev inequalities, convexity and Jensen's inequality, $p$-Yang-Mills fields, an extrinsic average variational method in the calculus of variation (cf.[W1, W3]) and $Φ_{(3)}$-harmonic maps, from varied, coupled, generalized viewpoints and perspectives (cf. Theorems 6.1, 7.1, 9.1, 9.2, 10.1,10.2, 11.13, 11.14, 11.15)).
