Characterization of convex sets
$begingroup$
Let $Omega subset mathbb{R}^n$ be a bounded domain. Is it true that
"$Omega$ is strictly convex $Leftrightarrow$ $forall p in partial Omega$ there exist a neighbourhood $U$ of $p$ and a strictly convex function $f : U cap partial Omega to mathbb{R}$"?
real-analysis general-topology convex-analysis
asked Jan 10 at 8:10
MichealMicheal
764
$endgroup$
add a comment |
$begingroup$
Let $Omega subset mathbb{R}^n$ be a bounded domain. Is it true that
"$Omega$ is strictly convex $Leftrightarrow$ $forall p in partial Omega$ there exist a neighbourhood $U$ of $p$ and a strictly convex function $f : U cap partial Omega to mathbb{R}$"?
real-analysis general-topology convex-analysis
asked Jan 10 at 8:10
MichealMicheal
764
$endgroup$
6
$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32
add a comment |
$begingroup$
Let $Omega subset mathbb{R}^n$ be a bounded domain. Is it true that
"$Omega$ is strictly convex $Leftrightarrow$ $forall p in partial Omega$ there exist a neighbourhood $U$ of $p$ and a strictly convex function $f : U cap partial Omega to mathbb{R}$"?
real-analysis general-topology convex-analysis
asked Jan 10 at 8:10
MichealMicheal
764
$endgroup$
Let $Omega subset mathbb{R}^n$ be a bounded domain. Is it true that
"$Omega$ is strictly convex $Leftrightarrow$ $forall p in partial Omega$ there exist a neighbourhood $U$ of $p$ and a strictly convex function $f : U cap partial Omega to mathbb{R}$"?
real-analysis general-topology convex-analysis
real-analysis general-topology convex-analysis
asked Jan 10 at 8:10
MichealMicheal
764
asked Jan 10 at 8:10
MichealMicheal
764
asked Jan 10 at 8:10
MichealMicheal
764
asked Jan 10 at 8:10
MichealMicheal
764
asked Jan 10 at 8:10
MichealMicheal
764
764
6
$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32
add a comment |
6
$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32
6
6
$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32
$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32
add a comment |
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$begingroup$
What do you mean for a function with domain $Ucap partialOmega$ to be (strictly) convex?
$endgroup$
– BigbearZzz
Jan 10 at 8:32