## Journals

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### Open Access Journals

DCDS

We give a positive lower bound for the principal curvature of the
strict convex level sets of harmonic functions in terms of the
principal curvature of the domain boundary and the norm of the
boundary gradient. We also extend this result
to a class of semi-linear elliptic partial differential equations under
certain structure condition.

DCDS

In this paper, we give two results concerning the positivity property of
the Paneitz operator-- a fourth order conformally covariant elliptic operator.
We prove that the Paneitz operator is positive for a compact Riemannian
manifold without boundary of dimension at least six if it has positve scalar
curvature as well as nonnegative $Q-$curvature. We also show that the positivity
of the Paneitz operator is preserved in dimensions greater than four in
taking a connected sum.

## Year of publication

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