Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: When a mapping is univalent (one-to-one) on a set is a question which has received considerable study. Much of the recent research has focused on the shape of the set on which the mapping is defined. It has been suggested, in fact, that the set must be convex for univalence to hold.  presents conditions under which the set need not be convex.  demonstrate first that the set can be diffeomorphic to a convex set and, second, that the set can have holes inside of it. These somewhat surprising results differ from previous results in that they depend not only upon the Jacobian, but also upon the function value. To provide further insight,  also examine the underlying geometry of the situation.
['Willard I. Zangwill']
I am writing a research paper on a idea Nonconvexities in Univalence
[{"from": "human", "value": "I am writing a research paper on a idea Nonconvexities in Univalence"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: When a mapping is univalent (one-to-one) on a set is a question which has received considerable study. Much of the recent research has focused on the shape of the set on which the mapping is defined. It has been suggested, in fact, that the set must be convex for univalence to hold.  presents conditions under which the set need not be convex.  demonstrate first that the set can be diffeomorphic to a convex set and, second, that the set can have holes inside of it. These somewhat surprising results differ from previous results in that they depend not only upon the Jacobian, but also upon the function value. To provide further insight,  also examine the underlying geometry of the situation."}]