Mixing
Convex curve has convex interior
$begingroup$
Let $c: mathbb{R} rightarrow mathbb{R}^2$ be a simple closed curve with curvature $kappa geq 0$.
Then the interior of $c$ is convex.
I know that in this case
$$
langle N(t_0), c(t) - c(t_0) rangle geq 0 quad text{for all}; t, t_0 in mathbb{R}.
$$
But how do I obtain that $text{Int}(c)$ is convex from there?
differential-geometry plane-curves
asked Jan 22 at 17:42
fpmoofpmoo
382113
$endgroup$
add a comment |
$begingroup$
Let $c: mathbb{R} rightarrow mathbb{R}^2$ be a simple closed curve with curvature $kappa geq 0$.
Then the interior of $c$ is convex.
I know that in this case
$$
langle N(t_0), c(t) - c(t_0) rangle geq 0 quad text{for all}; t, t_0 in mathbb{R}.
$$
But how do I obtain that $text{Int}(c)$ is convex from there?
differential-geometry plane-curves
asked Jan 22 at 17:42
fpmoofpmoo
382113
$endgroup$
add a comment |
$begingroup$
Let $c: mathbb{R} rightarrow mathbb{R}^2$ be a simple closed curve with curvature $kappa geq 0$.
Then the interior of $c$ is convex.
I know that in this case
$$
langle N(t_0), c(t) - c(t_0) rangle geq 0 quad text{for all}; t, t_0 in mathbb{R}.
$$
But how do I obtain that $text{Int}(c)$ is convex from there?
differential-geometry plane-curves
asked Jan 22 at 17:42
fpmoofpmoo
382113
$endgroup$
Let $c: mathbb{R} rightarrow mathbb{R}^2$ be a simple closed curve with curvature $kappa geq 0$.
Then the interior of $c$ is convex.
I know that in this case
$$
langle N(t_0), c(t) - c(t_0) rangle geq 0 quad text{for all}; t, t_0 in mathbb{R}.
$$
But how do I obtain that $text{Int}(c)$ is convex from there?
differential-geometry plane-curves
differential-geometry plane-curves
asked Jan 22 at 17:42
fpmoofpmoo
382113
asked Jan 22 at 17:42
fpmoofpmoo
382113
edited Jan 22 at 19:45
fpmoo
asked Jan 22 at 17:42
fpmoofpmoo
382113
asked Jan 22 at 17:42
fpmoofpmoo
382113
asked Jan 22 at 17:42
fpmoofpmoo
382113
382113
add a comment |
add a comment |
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