It is known that Teichmüller distance ($d_{Teich}$) on Teichmüller space is complete, whereas Weil-Petersson distance ($d_{WP}$) is not complete.
See for example the article
Wolpert, Scott. Noncompleteness of the Weil-Petersson metric for Teichmüller space. Pacific J. Math. 61 (1975), no. 2, 573--577 ,
in which Wolpert constructs an the explicit path on the Teichmüller space, which diverges in $d_{Teich}$, but converges in $d_{WP}$.
My question is : is it true in general that there is a positive constant $C$ such that $d_{WP} < C d_{Teich}$?
