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My question is about the support function defined $$s_{A}(x)= \sup \{x\cdot a | a \in A\}$$ ($A\subset R^{n}, x \in S^{n}$).(more generally it can be taken to be other scalar product.) So the function is defined on sets, and generally for the convex sets (as supporting hyperplanes are well used for exactly convex bodies). I just wanted to know if the following can be true or not. $$s_{A}(x) = s_{\partial A}(x)$$

I'm sorry if the quesion is inappropriate. Thank you.

kolobokish
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    Most often, the support function is restricted to convex compact sets. At least in this case, the answer is yes, boundary points suffice for defining the support function. – Jean Marie Nov 10 '16 at 18:35
  • @JeanMarie Thank you. Are there source I can read further about this? – kolobokish Nov 10 '16 at 18:37
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    There is a rather old book "Differential Geometry" by Heinrich W. Guggenheimer (Dover Ed.) which I find very nice with many results you hardly find elsewhere (in particular on support function), partly accessible as a google book. – Jean Marie Nov 10 '16 at 18:42

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