2025/08/18 by Karpenkov, Oleg, Müller, Christian, Pratoussevitch, Anna
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2508.13343
In this paper we study the stressability of semi-discrete frameworks in the plane which are generated by a discrete sequence of smooth curves. We characterize their stressability property by the existence of stresses fulfilling certain difference-differential equation. In particular, we define a semi-discrete height function which we use to generate liftings. Furthermore, we show a semi-discrete analogue of the Maxwell-Cremona lifting property which implies that the stressable semi-discrete frameworks in the plane are precisely the orthogonal projections of semi-discrete conjugate surfaces in 3-space. Finally, we discuss geometric implications for frameworks with vanishing boundary forces and characterize the liftability of frameworks which only consist of two neighboring curves forming one strip.