Piecewise minimal surfaces interpolating between two real analytic curves

TL;DR

This paper develops a method for constructing piecewise minimal surfaces that interpolate between two real analytic curves by using the Björling-Schwarz formula and inserting intermediate curves at specific points.

Contribution

It introduces a novel approach for creating piecewise minimal surfaces with prescribed boundary curves and intermediate interpolations using the Björling-Schwarz formula.

Findings

Existence of piecewise minimal surfaces interpolating between given curves.

Method for inserting intermediate curves to shape the surface.

Application of the Björling-Schwarz formula in this interpolation process.

Abstract

This paper is about interpolating minimal surfaces between two real analytic curves, a and b, each of which are simple real analytic curves, using the Bj\"{o}rling-Schwarz formula in the domain where it is valid, changing the normal distributions on inital curves. We insert curves $l_1,...l_L$ at specific locations and claim that there exists piecewise minimal surfaces interpolating between $a$ to $l_1$,$l_2$ to $l_3$, ...$l_L$ to $b