Skip to main content
MathOverflow

Return to Question

Commonmark migration
Source Link
Community Bot
Community Bot
  • 1
  • 2
  • 3

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible.

Questions.

 

(a) Is $E$ unique?

 

(b) If the answer is "yes", does the same hold for the analogous question in higher dimensions?

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible.

Questions.

 

(a) Is $E$ unique?

 

(b) If the answer is "yes", does the same hold for the analogous question in higher dimensions?

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible.

Questions.

(a) Is $E$ unique?

(b) If the answer is "yes", does the same hold for the analogous question in higher dimensions?

Notice removed Improve details by Wlodek Kuperberg
Bounty Ended with Jairo Bochi's answer chosen by Wlodek Kuperberg
Notice added Improve details by Wlodek Kuperberg
Bounty Started worth 200 reputation by Wlodek Kuperberg
added 38 characters in body
Source Link
T. Amdeberhan
T. Amdeberhan
  • 43.2k
  • 5
  • 57
  • 217

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible. Is $E$ unique? If the answer is "yes", does the same hold for the analogous question in higher dimensions?

Questions.

(a) Is $E$ unique?

(b) If the answer is "yes", does the same hold for the analogous question in higher dimensions?

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible. Is $E$ unique? If the answer is "yes", does the same hold for the analogous question in higher dimensions?

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible.

Questions.

(a) Is $E$ unique?

(b) If the answer is "yes", does the same hold for the analogous question in higher dimensions?

Source Link
Wlodek Kuperberg
Wlodek Kuperberg
  • 7.3k
  • 28
  • 60

Approximating a convex disk by an ellipse

For every convex compact set $K$ of area $1$ in $\mathbb{R}^2$, among all ellipses of area $1$ there exists an ellipse $E$ such that the area of the symmetric difference between $K$ and $E$ is smallest possible. Is $E$ unique? If the answer is "yes", does the same hold for the analogous question in higher dimensions?