There is an identity for the hyperbolic Riemann surfaces with at least one border. The identity is known as Generalized McShane Identity or Mirzakhani-McShane Identity proved by Mirzakhani in her seminal paper (Theorem 4.2). The questions are
Is there a similar kind of identity for the hyperbolic Riemann surfaces without any border and/or punctures?
For example, what is the WP volume of the moduli space of hyperbolic Riemann surfaces of genus two? How can we compute it?
