# Questions tagged [support-function]

For questions about the support function, a tool in convex geometry to represent sets via their support planes.

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### The support of the Schwarz rearrangement of a compactly supported function

Let $E \subset \mathbb{R}^N$ a measurable set of finite measure. We define $E^\ast$, the symmetric rearrangement of $E$ to be $$E^\ast := B_R(0), R = \left(\frac{|E|}{|B|}\right)^{\frac{1}{N}}.$$ ...
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### Support of function

As reported in https://en.wikipedia.org/wiki/Support_(mathematics), for a function $f:X \rightarrow \mathbb{R}$ we can define some notion of $supp(f)$, in particular: If $X$ is only a set, we define ...
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### Can we conclude that $g \in C_c (V)\$?

Let $U \subseteq \mathbb R^n$ be open and $f \in C_c (U).$ Let $V = U \cap B (0,1)$ be a non-empty open subset of $\mathbb R^n$ contained in $U.$ Can we conclude that $f \in C_c (V)\$? The support of ...
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### What is the support function of an ellipse?

I defined the support function $h_A:R^n→R$ of a non-empty closed convex set $A\subseteq \mathbb{R}^n$ as $$h_A(x)= \sup\left\{x⋅a |\ a \in A\right\}$$ Everything I know about this topic I found it. I ...
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