A Note on Constant Geodesic Curvature Curves on Surfaces

HUANG, Superhamonicity of curvatures for surfaces of constant mean curvature, Pacific J. HUANG - CHUN-CHI LIN, Negatively Curved Sets in Surfaces of

We extend recent existence results for compact constant mean curvature normal geodesic graphs with boundary in space forms in a unified way to a large class of ambient spaces1.

In [40], Petrunin developed an argument based on the second variation formula of arc-length and Hamitlon–Jacobi shift, and sketched a proof to the Lipschitz continuity of

Delano¨e [4] proved that the second boundary value problem for the Monge-Amp`ere equation has a unique smooth solution, provided that both domains are uniformly convex.. This result

Under the same condition, we prove that a non-closed ”flat” geodesic doesn’t exist, and moreover, there are at most finitely many flat strips, and at most finitely many

The result of Finn cited above presents a natural analogue of that theorem for surfaces of prescribed mean curvature; the present paper in turn extends the result to

Cover the compact segment v2v3 with a finite number of coordinate rectangles whose coordinate curves are lines of curvature... corresponding to part of the

exists and is a round sphere possibly degenerate, by the arguments from the proof of Lemma 4.3 and [8].. Since the sectional curvature of V i is bounded from below by K > 0,