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Likely the doubling of the disc is the best. Who can do better?

At least, if the diameter of the doubling is 1 then the average distance is bigger than $\tfrac12$. This shows that the optimal surface is not the round spher (i.e., the symmetry is not maximal). In this case, the chances that you will get an answer are nearly 0.

For example, the is a closely related problem of Alexandrov to maximize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer, the doubling of the disc is likely the best and the problem i open for more than 50 years.

Likely the doubling of the disc is the best. Who can do better?

At least, if the diameter of the doubling is 1 then the average distance is bigger than $\tfrac12$. This shows that the optimal surface is not the round sphere (in particular, the symmetry is not maximal). In this case, the chances to prove that the doubling of the disc (or any other candidate) is optimal are nearly 0.

For example, the is a closely related problem of Alexandrov to maximize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer, the doubling of the disc is likely the best and the problem is open for more than 50 years.

Likely the doubling of the disc is the best. Who can do better?

At least, if the diameter of the doubling is 1 then the average distance is bigger than $\tfrac12$. This shows that the optimal surface is not the round spher (i.e., the symmetry is not maximal). In this case, the chances that you will get an answer is nearly 0.

For example, the is a colsely related problem of Alexandrov to maximaize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer, the doubling of the disc is likely the best and the problem i open for more than 50 years.

Likely the doubling of the disc is the best. Who can do better?

At least, if the diameter of the doubling is 1 then the average distance is bigger than $\tfrac12$. This shows that the optimal surface is not the round spher (i.e., the symmetry is not maximal). In this case, the chances that you will get an answer are nearly 0.

For example, the is a closely related problem of Alexandrov to maximize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer, the doubling of the disc is likely the best and the problem i open for more than 50 years.

Likely the doubling of the disc is the best. Who can do better?

At least if its diameter of the doubling is 1 then the average bigger than $\tfrac12$. This shows that the optimal surface is not the round spher (i.e., the symmetry is not maximal). In this case the chances that you will get an answer is nearly 0.

For example, the is a colsely related problem of Alexandrov to maximaize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer and it is open for more than 50 years.

Likely the doubling of the disc is the best. Who can do better?

At least, if the diameter of the doubling is 1 then the average distance is bigger than $\tfrac12$. This shows that the optimal surface is not the round spher (i.e., the symmetry is not maximal). In this case, the chances that you will get an answer is nearly 0.

For example, the is a colsely related problem of Alexandrov to maximaize area among all the positively curved surfaces with diameter 1. The same picture --- round sphere is not the answer, the doubling of the disc is likely the best and the problem i open for more than 50 years.