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We show that a properly immersed minimal hypersurface in M × R+ equals some M×{c} when M is a complete, recurrent ndimensional Riemannian manifold with bounded curvature. If on the other hand,M is not necessarily recurrent but has nonnegative Ricci curvature with curvature bounded below, the same result holds for any positive entire minimal graph over M.

No abstract uploaded!

No abstract uploaded!

We derive a direct inversion formula for the exponential Radon transform. Our formula requires only the values of the transform over an 180° range of angles. It is an explicit formula, except that it involves a holomorphic function for which an explicit expression has not been found. In practice, this function can be approximated by an easily computed polynomial of rather low degree.