Tohoku Mathematical Journal
2004
March
SECOND SERIES VOL. 56, NO. 1

Tohoku Math. J.
56 (2004), 105-123

Title ON THE UNIQUE EXTREMALITY OF QUASICONFORMAL MAPPINGS WITH DILATATION BOUNDS

Author Yu-Liang Shen

(Received March 25, 2002, revised September 5, 2002)
Abstract. Concerning the problem of extremality of quasiconformal mappings with dilatation bounds, we discuss the unique extremality of the problem and prove the if part of a conjecture on the unique extremality ([G1], [R1]). To this end, we need to investigate a new extremal problem in the infinitesimal setting. In particular, we give a complete description of the unique infinitesimal extremality of partially zero Beltrami differentials.

2000 Mathematics Subject Classification. Primary 30F60; Secondly 32G15, 30C62, 30C70.
Key words and phrases. Quasiconformal mapping, Beltrami differential, uniquely extremal, uniquely infinitesimally extremal.

To the top of this page

Back to the Contents