Concept

Mean curvature

Related lectures (25)

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Plates II: Föppl-von Kármán Equations

Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.

Curve Tracing: Minimal Surfaces

Explores minimal surfaces and asymptotic lines on curved surfaces.

Course Recap and Asymptotic Grid Shells

Covers course recap, shape optimization, asymptotic grid shells, and differential geometry concepts.

Mean and Gaussian Curvature

Explores mean and Gaussian curvature, emphasizing their calculation for different bases and surfaces.

Differential Geometry of Surfaces

Covers the fundamentals of differential geometry of surfaces, including the equilibrium of shells, pressure vessels, and the curvature of surfaces.

Principal Curvatures and Mean Curvature

Explores principal curvatures, mean curvature, umbilical points, main curvatures, and eigenvalues.

Principal Curvatures: Gaussian Curvature

Explores principal curvatures and Gaussian curvature in the context of minimal surfaces, demonstrating their real-world applications.

Mechanics of Kirchhoff Rods: Finite Strain and Rotation Theory

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

Plates III: Mechanics of Slender Structures

Covers the equations of plates, bending and stretching energy, von Karman equations, and buckling of plates.

Gaussian Curvature in Plates

Explores Gaussian curvature, principal curvatures, and nonlinear strain in thin elastic plates.

Facial Modelling: An Interdisciplinary Approach

Explores interdisciplinary research in facial modelling, focusing on anatomical curves, valley curves, and Procrustes registration.

Discrete Differential Geometry

Covers topics in discrete differential geometry, including differential operators, Laplace-Beltrami operator, functions on triangle meshes, and discrete curvatures.

Surface Curvature and Assimilation

Explores surface curvature, curve assimilation, soap bubbles, capillarity, fluid mechanics, and types of flow.

Plates II: Föppl-von Kármán Equations

Explores the theory of plates, including bending and stretching energies, and the Föppl-von Kármán Equations.

Cylinders: Pressure and Geometry

Explores cylindrical pressure vessels, surfaces parametrization, and geometrical properties computation.

Surfaces with Variable Curvature

Explores surfaces with variable curvature, analyzing Gaussian and mean curvature, distinguishing convex and concave regions.

Plates II: Mechanics of Slender Structures

Explores the mechanics of slender structures, discussing plate evaluation, bending energy, and curvature tensors.

Normal Curvature

Explores normal curvature on a surface, discussing oriented curvature, existence proofs, and elimination methods for finding curvature.