V
主页
京东 11.11 红包
Jesse Madnick:A Gromov-Type Compactness Theorem in G2 Geometry——1
发布人
https://www.youtube.com/watch?v=JYfQyXqOBqs Da Rong Cheng, Spiro Karigiannis, Jesse Madnick——《Bubble Tree Convergence of Conformally Cross Product Preserving Maps》:https://doi.org/10.48550/arXiv.1909.03512 We study a class of weakly conformal 3-harmonic maps, called associative Smith maps, from 3-manifolds into 7-manifolds that parametrize associative 3-folds in Riemannian 7-manifolds equipped with G2-structures. Associative Smith maps are solutions of a conformally invariant nonlinear first order PDE system, called the Smith equation, that may be viewed as a G2-analogue of the Cauchy-Riemann system for J-holomorphic curves. In this paper, we show that associative Smith maps enjoy many of the same analytic properties as J-holomorphic curves in symplectic geometry. In particular, we prove: (i) an interior regularity theorem, (ii) a removable singularity result, (iii) an energy gap result, and (iv) a mean-value inequality. While our approach is informed by the holomorphic curve case, a number of nontrivial extensions are involved, primarily due to the degeneracy of the Smith equation. At the heart of above results is an ε-regularity theorem that gives quantitative C^{1,β}-regularity of W^{1,3} associative Smith maps under a smallness assumption on the 3-energy. The proof combines previous work on weakly 3-harmonic maps and the observation that the associative Smith equation demonstrates a certain "compensation phenomenon" that shows up in many other geometric PDEs. Combining these analytical properties and the conformal invariance of the Smith equation, we explain how sequences of associative Smith maps with bounded 3-energy may be conformally rescaled to yield bubble trees of such maps. When the G2-structure is closed, we prove that both the 3-energy and the homotopy are preserved in the bubble tree limit. This result may be regarded as an associative analogue of Gromov's Compactness Theorem in symplectic geometry.
打开封面
下载高清视频
观看高清视频
视频下载器
蔡徐坤 格莱美 Remedy [1080P]
在
Sodo的纹身
Bob历险记(三)爽番!
两年前的视频了兄弟萌
Dua Lipa at
好,但是如果当我30岁时我会看起来这么好,我等不及了
声音!控制!一切…… 完美!
Pada heran sih dia jadi peserta🥰🫶🏻最好的
Fugees • 用他的歌曲 @ musica轻轻地杀死我。频道
Escrito nas Estrelas • Lauana Prado
【fy—拉比克】我又K了吗?不可思议(Xm、Xxs、Karl)
今夕是何年 竟然还能看到肖战极乐净土的彩排
左奇函 X 杨博文《只对你有感觉》 focus
这麦是一点也不开啊
【林扬】跑来手势舞赛道扭一下(嘴唇白的像s了三天)
Punya temen beda pulau tu gak enak banget
【Ricky沈泉锐】猫师傅你是干什么工作的 4K高清《Feel The POP》饭拍|240812蔚山音乐节
黄龄的流氓转音有多狠?魅惑到需要打“马赛克”,开口就让人沦陷
so隔离编码
【周深南京810】哦说声嗨,我一定会来
Byliście na koncercie Kubana?
【Winky诗】人生无处不青山·深圳站
#russmillions #bigshark #fyp #NgabuburitGaya #serunyakuliner #serunyamembaca #Wo
我爱上她了
排名Travis Scott x 21 Savage歌曲!️
陈昊宇811裘德演唱会嘉宾全fo
【fy—发条】亚运都没选上,奥运能选上吗?
表妹说以后不想和我一起看演唱会了,说我达拉崩吧时要厥过去了
这他妈是55岁人能发出来的声音?
我所有的女孩slayy
回复 @ satwaalamliar脸颊!♂️
#消耗火 #bowdownandworshiphim#benjamindube #spiritofpraise #fyp #Jesus #值得
感觉自己
ti8回忆——fy
《真实的全开麦唱跳》话筒离开嘴是这个效果?
#CapCut #sia #bwp #foryourpage
让我们唱alooonggg
【fy—花仙子】我拿人头就是K的是吧(拒绝者、kaka、Emo、皮鞋、西红柿)
傅菁翻跳《Boom Boom Bass》,女生帅起来简直要命丨Go For You·贵阳场4K直拍