A distance comparison principle for evolving curves

Fréchet Distance for Curves, Revisited

We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo–output-s...

A comparison principle for minimizers

We give some conditions that ensure the validity of a Comparison principle for the minimizers of integral functionals, without assuming the validity of the Euler–Lagrange equation. We deduce a weak maximum principle for (possibly) degenerate elliptic equations and, together with a generalization of the bounded slope condition, the Lipschitz continuity of minimizers. To prove the main theorem we...

On the Hasse Principle for Shimura Curves

Let C be an algebraic curve defined over a number field K, of positive genus and without K-rational points. We conjecture that there exists some extension field L over which C violates the Hasse principle, i.e., has points everywhere locally but not globally. We show that our conjecture holds for all but finitely many Shimura curves of the form XD 0 (N)/Q or X D 1 (N)/Q, where D > 1 and N are c...

A Terminal Comparison Principle for Differential Inequalities

Average-distance problem for parameterized curves

We consider approximating a measure by a parameterized curve subject to length penalization. That is for a given finite compactly supported measure μ, with μ(R) > 0 for p ≥ 1 and λ > 0 we consider the functional