Questions tagged [hessian]

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Function of several variables whose hessian is a Hankel matrix

First of all, let me apologize because I asked this question a few days ago on https://math.stackexchange.com, but I did not get any reply. I am studying a function $f:\mathbb{R}^n\rightarrow\mathbb{R}...
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Hessian generating functions

I am looking for a characterization of functions $\Phi: \mathbb{R}^n \to \mathbb{R}^{n \times n}$ such that $\Phi(\mathbf{x}) = \nabla^2 f(\mathbf{x})$ for a function $f$ which is twice continuously ...
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1answer
116 views

Does there exist a real-valued function on the hyperbolic plane which has bounded hessian norm and unbounded gradient norm?

Does there exist a real-valued function on the hyperbolic plane which has bounded hessian norm and unbounded gradient norm? Specifically, consider the poincare half-plane model of the 2d hyperbolic ...
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Hessian formula for the sub manifold distance

I am working on some problems involving foliations and group actions and would be very nice to consider the second derivatives for the distance function of an orbit or a leaf. So my question is: does ...
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1answer
154 views

Does $f$ have the same minimiser as $\|\nabla f \|$ for $f$ strictly convex?

This question is migrated from MathStackExchange where it seemed to be too hard. I wonder does anyone here have any ideas? Suppose $f: K \to \mathbb R$ is $\mathcal C^2$ and strictly convex on some ...
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2answers
281 views

Product of concave functions and harmonic mean

I discovered something interesting, and I would like to know whether it is a known result or not. Say that a function $f: \Omega \subset \mathbb{R} \rightarrow \mathbb{R_+^*}$ is $\alpha$-concave if $...
3
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2answers
144 views

Factoring certain Hessians of real homogeneous bivariate polynomials

For any homogeneous polynomial $f \in \mathbb R [x,y]$, define the homogeneous polynomial $$H(f) := \partial_yf^2\partial_x\partial_xf-2\partial_xf\partial_yf\;\partial_x\partial_yf+\partial_xf^2\...