Conformal curvatures of curves in

Conformal diffeomorphisms and curvatures

In a study of Riemannian manifolds admitting conformal transformation, the Riemannian and Ricci curvatures play an important role for characterizations and classify such a manifold. In this note, we summarize known results about Riemannian manifold admitting conformal transformations and related topics.

Computation of Curvatures Using Conformal Parameterization

Curvatures on the surface are important geometric invariants and are widely used in different area of research. Examples include feature recognition, segmentation, or shape analysis. Therefore, it is of interest to develop an effective algorithm to approximate the curvatures accurately. The classical methods to compute these quantities involve the estimation of the normal and some involve the c...

Extremal Metrics for Conformal Curvatures on S

We define two conformal structures on S which give rise to a different view of the affine curvature flow and a new curvature flow, the “Qcurvature flow”. The steady state of these flows are studied. More specifically, we prove four sharp inequalities, which state the existences of the corresponding extremal metrics.

Conformal Images of Carleson Curves

We show that if γ is a curve in the unit disk, then arclength on γ is a Carleson measure iff the image of γ has finite length under every conformal map onto a domain with rectifiable boundary. Date: July 27, 2012. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

The Conformal Theory of Curves.