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Low-Dimensional Pinned Distance Sets Via Spherical Averages
The Journal of Geometric Analysis ( IF 1.2 ) Pub Date : 2021-05-12 , DOI: 10.1007/s12220-021-00686-1 Terence L. J. Harris
中文翻译:
通过球面平均值的低维固定距离集
更新日期:2021-05-13
The Journal of Geometric Analysis ( IF 1.2 ) Pub Date : 2021-05-12 , DOI: 10.1007/s12220-021-00686-1 Terence L. J. Harris
An inequality is derived for the average energies of pinned distance measures. This refines Mattila’s theorem on distance sets (Mattila in Mathematika 34:207–228, 1987) to pinned distance sets, and gives an analogue of Liu’s theorem (Liu in Geom Funct Anal 29:283–294, 2019) for pinned distance sets of dimension smaller than 1.
中文翻译:
通过球面平均值的低维固定距离集
固定距离量度的平均能量不等式导出。这将Mattila的距离集定理(Mattila in Mathematika 34:207–228,1987)细化为固定距离集,并给出了Liu定理的类似物(Liu in Geom Funct Anal 29:283–294,2019)类似的固定距离集。尺寸小于1。