1 Ju l 2 00 6 Analysis on Metric Space Q ∗
نویسنده
چکیده
In this paper, we show that the metric space (Q,G) is a positivelycurved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of (Q, G). Then we give a stratification of this metric space according to the signature of points in Q. Some properties of this stratification are shown. The second part of this paper is devoted to some basic analysis on the space (Q,G), like the direct sum and Lp space, which can be of independent interest. In the end, we give another definition of derivative for multiple-valued functions, which is equivalent to the one used by Almgren. An interesting theorem about regular selection of multiple-valued functions which preserves the differentiability concludes this paper.
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