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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. |
Jun
3 |
awarded | Teacher |
Jun
3 |
revised |
surfaces of constant centro-affine curvature
corrected spelling |
Jun
3 |
revised |
surfaces of constant centro-affine curvature
corrected spelling |
Jun
3 |
answered | surfaces of constant centro-affine curvature |
Jun
2 |
awarded | Editor |
Jun
2 |
revised |
How do control the boundary regularity of the Legendre transformation domain from a convex function
improved formatting |
Jun
2 |
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 |