ON CRITERION OF THE EXTREMALITY AND CONSTRUCTION OF HAMILTON SEQUENCES FOR A CLASS OF TEICHMULLER MAPPINGS |
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| Authors: | WU Zemin and LAI Wancai |
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| Institution: | Department of Applied Mathematics, Shanghai Jiaotong University, Shanghai 200030, China (permanent address is Department of Mathematics, Quanzhou Normal College, Quanzhou 362000, Fujian, China).;Department of Mathematics, Hua Qiao University, Quanzhou 362011, Fujian, China. |
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| Abstract: | It is proved that if f is a Teichmüller self-mapping of the unit disk with a holomorphic quadratic differential φ1, and φ satisfies the growth condition m(φ,r) = 1/2π f02π |φ(reiθ)| dθ =o((1 - r)-s), r → 1, for any s ＞ 1, then f is extremal, and there exists a sequence {tn}, 0 ＜ tn ＜ 1, lim tn = 1, such that {φ(tnz)} is a Hamilton sequence. It is the precision of a n→∞ theorem of Reich-Strebel in 1974, and gives a fairly satisfactory answer to a question of Reich in 1988. |
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| Keywords: | Extremality Hamilton sequence |
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