A Zoo of Dualities
نویسندگان
چکیده
Abstract In this note we study order reversing quasi involutions and their properties. These maps are dualities (order involutions) on image. We prove that any involution is induced by a cost. Invariant sets of special interest provide several results regarding existence uniqueness. determine when an sub-class can be extended to the whole space discuss uniqueness such extension. also ways for constructing new from given ones. particular, define dual order-reversing quasi-involution. Finally, throughout paper exhibit “zoo” illustrative examples. Some them classical, some have recently attracted attention convexity community new. in depth example polarity obtain Blaschke-Santaló type inequality corresponding Gaussian volume product. The unified point view presented gives deeper understanding underlying principles structures, offering exciting perspective topic, exposing many research directions.
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ژورنال
عنوان ژورنال: Journal of Geometric Analysis
سال: 2023
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-023-01302-0