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Jun
5
comment How do control the boundary regularity of the Legendre transformation domain from a convex function
In my question, f(x) may be defined on the whole $\mathbb{R}^n$ (this situation is my interest), for example, the following function (known as hyperbolic affine hypersphere): $$f(x_1,...,x_n)=\frac{1}{x_1\cdots x_n}, x_i>0, 1\leq i\leq n.$$ Choose suitable coordinates, this graph can be represented by another function $\tilde{f}$ defined on the whole $\mathbb{R}^n$, and the Legendre transformation domain of $\tilde{f}$ is a simplex.
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3
awarded  Teacher
Jun
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revised surfaces of constant centro-affine curvature
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Jun
3
revised surfaces of constant centro-affine curvature
corrected spelling
Jun
3
answered surfaces of constant centro-affine curvature
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revised How do control the boundary regularity of the Legendre transformation domain from a convex function
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asked How do control the boundary regularity of the Legendre transformation domain from a convex function
May
30
answered Solutions to a Monge-Ampère equation on the simplex