Title: On the Fenchel problem of level sets

In the lecture, a new and "nice" geometric necessary and sufficient condition will be given for the existence of a smooth convex function with the level sets of a given smooth pseudoconvex function. The main theorem is proved by using a general differential geometric tool, the geometry of path defined on smooth manifolds. This approach provides a new view on the convexlike and generalized convexlike mappings in the image analysis, and a complete geometric characterization of a new subclass of pseudoconvex functions originated from analytical mechanics.
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