Uniqueness of Hamiltonian volume minimizing Lagrangian submanifolds which are Hamiltonian isotopic to RP^n in CP^n
Hiroshi Iriyeh
本文证明了CP^n模等距群作用中与RP^n哈密尔顿同构的哈密尔顿体积极小化拉格朗日子流形的唯一性.
The purpose of this short note is to prove the uniqueness of Hamiltonian volume minimizing Lagrangian submanifolds which are Hamiltonian isotopic to RP^n in CP^n modulo isometric group actions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Area-minimizing submanifolds are not generically smooth
本文证明面积最小化子流形并非一般光滑，解决White猜想，并给出其奇异集Hausdorff维数的下界$\max\{d-5,d-c\}$。
On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold
本文证明在几乎所有光滑流形上都存在具有分形奇点集的面积最小子流形，解决了阿尔梅伦猜想的部分问题。
We show that every area-minimizing hypercone and every oriented Lawlor cone in [Law91] can be realized as a tangent cone at a point of some homologically area-minimizing singular compact submanifold. In particular this generalizes the result of N. Smale [Sma99].
On a conjecture of Almgren: area-minimizing submanifolds with fractal singularities
本文在紧致黎曼流形上构造了具有分形奇点集的面积最小子流形，精确解决了Almgren猜想，并能任意指定奇点集的Almgren分层，结果适用于多种流和varifold范畴。
Area-minimizing submanifolds are not generically smooth, except for geodesics, minimal surfaces, and minimal hypersurfaces
研究模2同调中面积最小化子流形的光滑性，证明其一般非光滑（除特定情况），解决怀特猜想，还建立奇异集豪斯多夫维数下界，并证明$\rpt$维罗内塞极小嵌入上的锥是模2面积最小化的。
Some configuration results for area-minimizing cones
本文研究了构造面积最小锥体的配置结果，发现特定条件下的极小子流形和球面的乘积锥体具有面积最小性质，并证明了相关类别的基数相同。
Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces $-$ minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones. They are cones over focal submanifolds and cones over suitable products among these two classes. Except in low dimensions, all such cones are shown minimizing.
The Hasse Principle for Geometric Variational Problems: An Illustration via Area-minimizing Submanifolds
本文探讨了几何变分问题中Hasse原理的应用，通过面积最小子流形展示了如何从实同调和模n同调中恢复积分同调中的信息，并回答了Almgren等人提出的问题。
Suppose that $N$ is a smooth manifold with a smooth Riemannian metric $g_0$, and that $Γ$ is a smooth submanifold of $N$. This paper proves that for a generic (in the sense of Baire category) smooth metric $g$ conformal to $g_0$, if $F$ is any simple $g$-minimal immersion of a closed manifold into N, then $F$ is transverse to $Γ$ and $F$ is self-transverse. The theorem remains true with "transverse" and "self-transverse" replaced by "strongly transverse" and "strongly self-transverse". The theorem also holds for hypersurfaces of constant mean curvature or, more generally, of prescribed mean cu…
Lagrangian submanifolds and Lefschetz pencils
给定辛流形中的一个拉格朗日子流形和子流形上的Morse函数，我们证明了流形上存在一个同位Morse函数和一个辛Lefschetz束，将Morse函数推广到整个流形.从这个结构中，我们定义了一个序列的辛不变量分类的合痕类的拉格朗日球在辛4流形。
Interior regularity of area minimizing currents within a $C^{2,α}$-submanifold
本文证明了在 $C^{2,α}$ 类嵌入子流形内，面积极小整流的内部奇异集的 Hausdorff 维数不超过 $m-2$，确立了任意余维数下该流的内部正则性理论。
Lagrangian two-spheres can be symplectically knotted
本文证明了辛四流形M具有以下性质：M中的光滑嵌入双球面的一个合痕类包含无穷多个拉格朗日子流形，其中没有两个子流形是同素的拉格朗日子流形.这些例子是使用一类特殊的辛自同构（“广义德恩扭曲”）构造的。证明使用了弗洛尔同调。修订版本：删除一个脚注，增加一个参考资料
A proof of the Hamiltonian Thom Isotopy Lemma
本文针对紧辛流形中单参数紧辛子流形族，给出其所有成员彼此 Hamiltonian 同痕这一结论的完整证明。
The chord conjecture for conormal bundles
本文通过建立环绕Floer上同调与路径空间同调的同构，并结合扭曲Hurewicz定理，证明了闭流形余球丛中与余法丛同位素的Legendre子流形均满足Arnol'd弦猜想。
Unlinking and unknottedness of monotone Lagrangian submanifolds
该研究在特定拓扑假设下证明了同单调性常数的单调拉格朗日子流形的无环绕性与纽结类型由同伦论数据决定，并推导出复维数≥5的奇数维辛向量空间中所有单调拉格朗日环面光滑同痕。
The paper studies how to extend local calibration pairs to global ones in various situations. As a result, new discoveries involving mass-minimizing properties are exhibited. In particular, we show that a $\mathbb R$-homologically nontrivial connected submanifold $M$ of a smooth Riemannian manifold $X$ is homologically mass-minimizing for some metrics in the same conformal class. Moreover, several generalizations for $M$ with multiple connected components or for a mutually disjoint collection (see §3.5) are obtained. For a submanifold with certain singularities, we also establish an extension …
Maslov class rigidity for Lagrangian submanifolds via Hofer's geometry
在这项工作中，我们建立了新的刚性结果的Maslov类的拉格朗日子流形在大类的封闭和凸辛流形。我们的主要结果建立了上界的最小Maslov数的移位拉格朗日子流形，这是产品流形的因素，每个承认一个度量的负截面曲率。这样的拉格朗日子流形存在于维度大于6或等于4的每个辛流形中。证明利用了拉格朗日上的闭测地线，拉格朗日附近支持的几何Hamilton流的周期轨道，以及这些流关于负Hellmann长度泛函的长度极小化性质之间的关系.
We study lower semi-continuity properties of the volume, i.e., the surface area, of a closed Lagrangian manifold with respect to the Hofer- and $γ$-distance on a class of monotone Lagrangian submanifolds Hamiltonian isotopic to each other. We prove that volume is $γ$-lower semi-continuous in two cases. In the first one the volume form comes from a Kähler metric with a large group of Hamiltonian isometries, but there are no additional constraints on the Lagrangian submanifold. The second one is when the volume is taken with respect to any compatible metric, but the Lagrangian submanifold must b…
On the uniqueness of tangent cones to area minimizing currents at boundaries with arbitrary multiplicity
本文证明任意整数边界重数的面积最小化流在密度 $Q/2$ 边界点处切锥唯一且收敛具有幂次速率，并由此导出支撑高重数边界正则性理论的分解定理。
Excess decay for minimizing hypercurrents mod $2Q$
本文证明了模偶数 $p=2Q$ 的面积极小超流在 Riemannian 子流形中的最优余亏衰减估计，该技术改进为证明其奇异集的特定维数分解提供了关键支撑。
We obtain families of non-isotopic closed exact Lagrangian submanifolds in quasi-projective holomorphic symplectic manifolds that admit contracting $\mathbb{C}^*$-actions. We show that the Floer cohomologies of these Lagrangians are topological in nature, recovering the ordinary cohomologies of their intersection. Moreover, by using these Lagrangians and a version of Carrell-Goresky's integral decomposition theorem, we obtain degree-wise lower bounds on the symplectic cohomology of these spaces.
On a Problem Posed by Brezis and Mironescu
本文解决了一个关于面积最小积分可测电流与光滑子流形面积下界的问题，证明了两者在特定条件下相等。
Length minimizing Hamiltonian paths for symplectically aspherical manifolds
本文研究辛非球面流形上拟自治Hamilton算子生成的Hamilton路的长度极小化性质。受L. Polterovich和M. Schwarz，我们研究了生成哈密顿量的Floer复形中固定全局极值的作用。我们的主要结果确定了一个自然的条件上的一个固定的全局极大值的哈密顿量，这意味着相应的道路最小化的积极的哈登长度。我们用它来证明，一个准自治哈密顿产生的长度最小化的道路，如果它有下扭曲的固定的全球极值和没有周期轨道与周期1和行动大于的固定极值。这反过来又使我们能够产生新的例子，自治的哈密顿流的长度最小化的所有时间。这些构造是基于余迷向子流形的几何。最后给出了D. McDuff，其中指出，准自治哈密顿在短时间间隔内生成长度最小化路径。
Singularities of Lagrangian mean curvature flow: zero-Maslov class case
研究了当初始条件为零Maslov类拉格朗日量时，$\C^n$中拉格朗日中曲率流的奇异性.我们首先要说明，在这种情况下，奇点是不可避免的。更确切地说，我们构造拉格朗日与任意小的拉格朗日角和拉格朗日是哈密顿同位素的平面，然而，开发有限的时间奇点下中曲率流。然后，我们证明了两个定理关于切流在奇点时的初始条件是零马斯洛夫类拉格朗日。第一个（定理A）指出，在奇点处的重标度流弱收敛到面积最小化拉格朗日锥的有限并。第二个定理（定理B）指出，在初始条件是几乎校准和有理拉格朗日的附加假设下，重新标度流的连通分量收敛到单个面积最小化拉格朗日锥，而不是面积最小化拉格朗日锥的可能非面积最小化并集。后一个条件是稠密的拉格朗日与生成的$H_1(L,\Z)$。
An essential one sided boundary singularity for a $3$-dimensional area minimizing current in $\mathbb{R}^5$
本文构造了 $\mathbb{R}^5$ 中具有平坦切锥的本质单侧边界奇点的 $3$ 维面积极小流，证明了高边界重数下的边界正则性理论在维度上是精确的，并发展了相关边界正则性理论。
Consider an area minimizing current modulo $p$ of dimension $m$ in a smooth Riemannian manifold of dimension $m+1$. We prove that its interior singular set is, up to a relatively closed set of dimension at most $m-2$, a $C^{1,α}$ submanifold of dimension $m-1$ at which, locally, $N\leq p$ regular sheets of the current join transversally, each sheet counted with a positive multiplicity $k_i$ so that $\sum_i k_i = p$. This completes the analysis of the structure of the singular set of area minimizing hypersurfaces modulo $p$, initiated by J. Taylor for $m=2$ and $p=3$ and extended by the authors…
Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows
我们构造了拉格朗日中曲率流的收缩器和扩张器的例子。这些例子是哈密尔顿平稳和渐近联盟的两个哈密尔顿固定锥发现Schoen和沃尔夫森。Schoen-Wolfson锥$C_{p,q}$是变分方法中特殊拉格朗日量或拉格朗日极小曲面存在性问题的障碍。已知这些锥奇点不能由任何光滑定向的拉格朗日子流形来解决。我们发现的收缩器和扩张器可以粘合在一起，产生Brakke运动的解--中曲率流的弱公式。对于除$(2,1)$以外的任何互质对$(p,q)$，我们构造了这样一个解，它能分解任何单个Schoen-Wolfson锥$C_{p,q}$ .因此，这为Schoen-Wolfson猜想提供了证据，即$(2,1)$锥是唯一的面积最小化锥。也得到了高维推广。
Area minimizing hypersurfaces modulo $p$: a geometric free-boundary problem
本文研究完备 Riemann 流形中模 $p$ 面积极小流的局部结构，证明其向具有脊的切锥唯一收敛并衰减，从而给出奇数模数及偶数模数相应条件下的自由边界分解。
On the regularity of area minimizing currents at boundaries with arbitrary multiplicity
本文将 Allard 边界正则性定理推广到任意重数的面积最小化积分流，刻画密度 Q/2 奇异边界点的可求长性，并在凸障碍条件下得到整个边界奇异集的维数估计。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。