MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

How to compute the first eigenvalue of hyperbolic space ${H^2}$and ${H^n}$?

share|cite|improve this question

Of which operator? The Laplacian? If so it is related to the right regular representation of Sl(n,R) or rather to the unramified, tempered, unitary reps. The spectrum is continuous and [1/4, \infty) for n =2. The situation is similar in higher rank, but 1/4 has to be replaced by something else (I don't recall what exactly). In fact, the eigenvectors can be written down explicitly in all cases.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.