球面与复射影空间的度量测度极限
Metric measure limits of spheres and complex projective spaces
摘要：
研究了无界维数球面序列和复射影空间的极限。一系列球体（分别为复射影空间）要么是Levy族，要么是无穷耗散的，要么是收敛于（或的霍普夫商）一个虚拟的无限维高斯空间，取决于空间的大小。这些是第一个发现的例子，其性质是极限与序列中的空间截然不同。为了证明这一点，我们在度量测度空间的Gromov紧化上引入了一个度量。
英文摘要：
We study the limits of sequences of spheres and complex projective spaces with unbounded dimensions. A sequence of spheres (resp. complex projective spaces) either is a Levy family, infinitely dissipates, or converges to (resp. the Hopf quotient of) a virtual infinite-dimensional Gaussian space, depending on the size of the spaces. These are the first discovered examples with the property that the limits are drastically different from the spaces in the sequence. For the proof, we introduce a metric on Gromov's compactification of the space of metric measure spaces.
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