The author wishes to express his gratitude to the anonymous referees, whose suggestions and constructive criticisms led to substantial improvements in the presentation. Moreover, I thank Franco Fagnola and Roberto Quezada for helpful comments.
We will concern only with a pair of quadratic forms in Rn, and use the notation introduced in Section 2. It seems to be the convexity Dines theorem was conceived once Dines awares the following result, known as (strict) Finsler’s theorem: if
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