无散度浓度来自消失序列
Divergence-free concentrations come from vanishing sequences
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中文总结 AI 辅助
本文在非对称情形下证明了 Bouchitté 消失质量猜想的逆命题：任何由奇异矩阵重心微结构叠加而成的极限分布均可由无散度消失序列实现，且可构造支撑在体积趋于零的开集上、边界光滑的场。
中文摘要 AI 辅助
一个无散度矩阵场的消失序列 $V_n$ 是指在 $L^1$ 中有界且由体积趋于零的开集 $A_n$ 承载的序列。近期确立的 Bouchitté 消失质量猜想指出，这样的序列所能承载的方向受到刚性约束：其极限分布必须是微结构的叠加，而这些微结构的重心是奇异矩阵。我们在非对称情形下证明了其逆命题：每一个这样的叠加都可以由一个消失序列实现。事实上，我们能够构造出支撑在 $A_n$ 上的无散度场 $V_n$，其相对边界是一个光滑紧流形。
英文摘要
A vanishing sequence $V_n$ of divergence-free matrix fields is one that is bounded in $L^1$ and is carried by open sets $A_n$ of vanishing volume. Recently established, Bouchitté's vanishing mass conjecture says that the directions such a sequence can carry are rigidly constrained: their limiting distribution must be a superposition of microstructures whose barycenters are singular matrices. We prove the converse in the non-symmetric setting: every such superposition is attained by a vanishing sequence. In fact, we are able to construct divergence-free fields $V_n$ $supported$ on $A_n$, whose relative boundary is a smooth compact manifold.
发表机构
- Dipartimento di Matematica, Università di Pisa（比萨大学数学系）
- Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II（那不勒斯费德里科二世大学数学与应用科学系）
机构由 AI 辅助整理，请以论文原文为准。
