Related papers: Convergence Analysis of Dirichlet Energy Minimizat…
In this paper, we first extend the finite distortion problem from the bounded domains in $\mathbb{R}^2$ to the closed genus-zero surfaces in $\mathbb{R}^3$ by the stereographic projection. Then we derive a theoretical foundation for…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
Conformal energy minimization is an efficient approach to compute conformal parameterization. In this paper, we develop a stable algorithm to compute conformal parameterization of simply connected open surface, termed Stable Discrete…
Let $N=(\Omega,\sigma)$ and $M=(\Omega^*,\rho)$ be doubly connected Riemann surfaces and assume that $\rho$ is a smooth metric with bounded Gauss curvature $\mathcal{K}$ and finite area. The paper establishes the existence of homeomorphisms…
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…
Let $\mathbb{A}$ and $\mathbb{A_{*}}$ be two non-degenerate spherical annuli in $\mathbb{R}^{n}$ equipped with the Euclidean metric and the weighted metric $|y|^{1-n}$, respectively. Let $\mathcal{F}(\mathbb{A},\mathbb{A_{*}})$ denote the…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We extend the celebrated theorem of Kellogg for conformal diffeomorphisms to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between doubly connected Riemanian…
Continuous conformal transformation minimizes the conformal energy. The convergence of minimizing discrete conformal energy when the discrete mesh size tends to zero is an open problem. This paper addresses this problem via a careful error…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…
The study of singular perturbations of the Dirichlet energy is at the core of the phenomenological-description paradigm in soft condensed matter. Being able to pass to the limit plays a crucial role in the understanding of the…
We propose a new effective method called spherical authalic energy minimization (SAEM) for computing spherical area-preserving parameterizations of genus-zero surfaces. The proposed SAEM has solid theoretical support and guaranteed…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional in the class of $\mathbb{S}^2$-valued maps defined in cylindrical surfaces. The model naturally arises as a curved thin-film limit in the theories of…
Surface parameterizations are widely applied in computer graphics, medical imaging and transformation optics. In this paper, we rigorously derive the gradient vector and Hessian matrix of the discrete conformal energy for spherical…
We consider the approximation of minimal geodesics between two closed sets in $\mathbb{R}^D$ endowed with a smooth Riemannian metric. The continuous problem is formulated as the minimization of the energy functional over piecewise smooth…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline, and propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings. Specifically, we first…
We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…