Maybe you are asking for uniqueness, not existence? Then the answer is yes because your metric admits a locally CAT(0) completion in the answer abovebelow. This uniqueness result, originally, I think, due to Teichmuller, should be also in Strebel's book and is based on a Gauss-Bonnet calculation.
|
2 | added 140 characters in body | ||
|
|
||||
|
|
1 |
|
||
|
Maybe you are asking for uniqueness, not existence? Then the answer is yes because your metric admits a locally CAT(0) completion in the answer above. |
||||
