Abstract
For a non-tangential slit (t), the behavior of the driving function �(t) near zero in the Loewner equation is well understood; for tangential slit, the situation is less clear. In this paper, we investigate the tangential slit p , p > 0, where is a circular arc tangent at 0; p has order p+1 p near zero. Our main result is to give the exact expression of �(t), and its Holder exponent near 0 in terms of p, which has a natural connection with the known results. We also extend this to a general type of tangential slits, and give an estimation of the growth of �(t) near 0.
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