On the curvature of an inner curve in a Schwarz-Christoffel mapping

• In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-­Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded. In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-­Christoffel mapping from R, the unit disk or upper half­plane, to a polygonal region P of a curve inside R. From the Schwarz-­Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

curvature

Schwarz-Christoffel mapping

inner curve

outer polygon

Mathematical analysis

Analys

Applied mathematics

Tillämpad matematik

Numerical analysis

Numerisk analys

Mathematics

Matematik

Publication and Content Type

vet (subject category)

rap (subject category)