Non-decreasable extremal Beltrami differentials of non-landslide type

Abstract

In this paper, we deform a uniquely-extremal Beltrami differential into different non-decreasable Beltrami differentials, and then construct non-unique extremal Beltrami differentials such that they are both non-landslide and non-decreasable.

Extremal Beltrami Differentials of Non-Landslide Type

“…Actually, up to the present time, no extremal with (A)+(C) can be found in the literature. Recently, the author constructed a non-unique extremal example for (A)+(C)+(NB) in a preprint [15]. To sum up, the only case for which we give no examples is (A)+(B)+(C).…”

Nondecreasable and Weakly Nondecreasable Dilatations

“…We find that they vanish on certain subdomains in ∆ and hence all of them are of landslide type. Recently, the author constructed certain nondecreasable nonuniquely extremal dilatation of nonlandslide type by use of the main inequality in [17]. Naturally, we ask the following question.…”