Two results for symphonic maps under assumptions on m-symphonic energy
Two results for symphonic maps under assumptions on m-symphonic energy
复制标题
m-交响能量假设下交响映射的两个结果
DOI：
10.1007/s00025-022-01741-1
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发表时间：
2022
影响因子：
2.2
通讯作者：
Nobumitsu Nakauchi
中科院分区：
文献类型：
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作者：
佐藤進;佐藤進;Nobumitsu Nakauchi;Nobumitsu Nakauchi;Nobumitsu Nakauchi
我们通过黎曼流形之间的平滑映射来考虑度量回调的能量函数。静止地图被称为交响地图，并在 Kawai 和 Nakauchi (Nonlinear Anal 74:2284–2295, 2011; Differ Geom Appl 44:161–177, 2016; Differ Geom Appl 65:147–159, 2019)、Misawa 和 Nakauchi (Nonlinear Anal) 进行了研究75:5971–5974, 2012; Calc Var Partial Differ Equ 55:1–20, 2016; Adv Differ Equ 23:693–724, 2018; Part Differ Equ Appl 2:19, 2021) 和 Nakauchi 和 Takenaka (Ricerche Matematica 60:219–235) 2011）。在本文中，我们关注的是它们-交响能量，即交响能量的-版本，其中m表示源流形M的维数。它们的交响能量是保形不变的，并在 Misawa 和 Nakauchi 中引入（Part Differ Equ Appl 2:19, 2021）。在这种共形能量的某些条件下，我们给出了交响映射的两个结果：间隙定理和刘维尔型定理。
We consider the-energy functionalof pullbacks of metrics by smooth mapsfbetween Riemannian manifolds. Stationary maps forare calledsymphonic mapsand researched in Kawai and Nakauchi (Nonlinear Anal 74:2284–2295, 2011; Differ Geom Appl 44:161–177, 2016; Differ Geom Appl 65:147–159, 2019), Misawa and Nakauchi (Nonlinear Anal 75:5971–5974, 2012; Calc Var Partial Differ Equ 55:1–20, 2016; Adv Differ Equ 23:693–724, 2018; Part Differ Equ Appl 2:19, 2021) and Nakauchi and Takenaka (Ricerche Matematica 60:219–235, 2011). In this paper we are concerned with them-symphonic energy, i.e., the-version of the symphonic energy, wheremdenotes the dimension of the source manifoldM. Them-symphonic energy is conformally invariant and is introduced in Misawa and Nakauchi (Part Differ Equ Appl 2:19, 2021). Under some conditions on this conformal energy, we give two results—a gap theorem and a Liouville type theorem—for symphonic maps.