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Mixed surface area measures
To each \((n-1)\) -tuple...
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The Covering Radius and a Discrete Surface Area for Non-Hollow Simplices
We explore upper bounds on the covering radius of non-hollow lattice polytopes. In particular, we conjecture a general upper bound of d /2 in...
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Investigation of Light Scattering by Plasmonic Core-Shell Nanoparticles via the Discrete Sources Method Accounting for the Surface Quantum Effect
AbstractIn this paper, we investigate the influence of the surface quantum effect on the absorption cross section and the field enhancement factor of...
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Discrete Yamabe Problem for Polyhedral Surfaces
We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical...
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Trivalent Discrete Surfaces
In the previous chapter, we explained “negatively” curved carbon structure; however, the definition of negativity is that the total curvature or the...
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Surface area measures of log-concave functions
This paper’s origins are in two papers: One by Colesanti and Fragalà studying the surface area measure of a log-concave function, and one by...
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Deformation of discrete conformal structures on surfaces
In Glickenstein (J Differ Geom 87: 201–237, 2011), Glickenstein introduced the discrete conformal structures on polyhedral surfaces in an axiomatic...
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Boundary metric of Epstein-Penner convex hull and discrete conformality
The Epstein-Penner convex hull construction associates to every decorated punctured hyperbolic surface a convex set in the Minkowski space. It works...
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Discrete Weierstrass-Type Representations
Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We...
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The geometry of discrete asymptotic-geodesic 4-webs in isotropic 3-space
The geometry of webs has been investigated over more than a century driven by still open problems. In our paper we contribute to extending the...
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Volume and area
The notions of “length”, “area”, and “volume” describe and yield central topics in various mathematical fields, especially also in geometry.
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Discrete Isothermic Nets Based on Checkerboard Patterns
This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It...
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A Structure-Preserving Parametric Finite Element Method for Area-Conserved Generalized Curvature Flow
A structure-preserving numerical method is presented and analyzed to simulate the motion of closed curves governed by area-conserved generalized...
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The Origins of Discrete Diversity
The p-dispersion facility location problem first emerged in the 1970s as a byproduct of covering and center location problems and the dual...
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Aerodynamic/stealth design of S-duct inlet based on discrete adjoint method
It is a major challenge for the airframe-inlet design of modern combat aircrafts, as the flow and electromagnetic wave propagation in the inlet of...
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The Convergence of Discrete Uniformizations for Genus Zero Surfaces
The notion of discrete conformality proposed by Luo (2004) and Bobenko et al. (2015) on triangle meshes has rich mathematical theories and wide...
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Discrete cyclic systems and circle congruences
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate...
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Nodal Auxiliary Space Preconditioning for the Surface de Rham Complex
This work develops optimal preconditioners for the discrete H (curl) and H (div) problems on two-dimensional surfaces by nodal auxiliary space...
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A Projection Method Based on Discrete Normalized Dynamical System for Computing C-eigenpairs
The largest C-eigenvalue of piezoelectric tensors determines the highest piezoelectric coupling constant, which reflects the coupling between the...
