无限正牛顿共形度量在角点附近的完备纤维
Completion Fibres of Infinite Positive Newton Conformal Metrics Near Corners
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中文总结 AI 辅助
本文研究余维二角点附近正奇异共形度量的局部完备化，发现临界幂次时需拉普拉斯变换补充支撑几何，并给出纤维空或单点的判定及多种相关性质。
中文摘要 AI 辅助
我们研究了当共形因子由指数空间上的紧致正测度生成时，余维数为二的角点附近正奇异共形度量的局部度量完备化。牛顿支撑函数决定了非临界加权射线可达性，但在临界幂次阶时，仅凭支撑几何信息是不够的。我们识别出缺失的不变量为拉普拉斯变换，它度量了指数质量如何趋近临界全次数的面。若最大全次数大于2，则角点上的局部完备纤维为空。当所有全次数至多为2时，纤维为空或为单点，分别取决于临界拉普拉斯剖面的平方根在无穷远处是否可积。我们给出了支撑相同但临界完备行为相反的测度、尖锐性例子、单调截断现象、内蕴Lipschitz完备坐标，以及适用于牛顿可比密度的双Lipschitz传递原理。
英文摘要
We study the local metric completion of positive singular conformal metrics near a codimension-two corner when the conformal factor is generated by a compact positive measure on exponent space. The Newton support function determines noncritical weighted-ray accessibility, but at the critical power order support geometry alone is insufficient. We identify the missing invariant as a Laplace transform measuring how exponent mass approaches the critical total-degree face. If the maximal total degree exceeds 2, the local completion fibre over the corner is empty. When all total degrees are at most 2, the fibre is empty or a singleton according as the square root of the critical Laplace profile is nonintegrable or integrable at infinity. We give support-identical measures with opposite critical completion behaviour, sharpness examples, monotone truncation phenomena, intrinsic Lipschitz completion coordinates, and a bi-Lipschitz transfer principle for Newton-comparable densities.
