A Frequency Function and Singular Set Bounds for Branched Minimal Immersions
نویسندگان
چکیده
منابع مشابه
Moduli for Spherical Eigenmaps and Minimal Immersions
Eigenmaps and spherical minimal immersions of round spheres into round spheres form an interesting subject that has been studied by many authors. The components of an eigenmap are eigenfunctions of the Laplace-Beltrami operator on Sm, the Euclidean m-sphere, m ≥ 2; and the eigenfunctions correspond to a fixed eigenvalue λk, k ≥ 1. Given m ≥ 2 and k ≥ 1, these eigenmaps can be parametrized by a ...
متن کاملThree Bounds on the Minimal Singular Value: A Comparison
We presented a new lower bound on minimal singular values of real matrices based on Frobenius norm and determinant and showed in [4] that under certain assumptions on the matrix is our estimate sharper than a recent lower bound from Hong and Pan [3]. In this paper we show, under which conditions is our lower bound sharper than two other recent lower bounds for minimal singular values based on a...
متن کاملCompact Complete Minimal Immersions In
ANTONIO ALARC´ON ABSTRACT. In this paper we construct complete minimal surfaces with boundary in R 3 of arbitrary finite topology. For any arbitrary finite topological type we find a compact Riemann surface M, an open domain M ⊂ M with the fixed topological type, and a conformal complete minimal immersion X : M → R 3 which can be extended to a continuous map X : M → R 3 , such that X |∂M is an ...
متن کاملCR Singular Immersions of Complex Projective Spaces
Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification. A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils. Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex pr...
متن کاملCritical Points of the Distance Function on the Moduli Space for Spherical Eigenmaps and Minimal Immersions
The boundary of a DoCarmo-Wallach moduli space parametrizing (harmonic) eigenmaps between spheres or spherical minimal immersions carries a natural stratification. In this paper we study the critical points of the distance function on the boundary strata. We show that the critical points provide a natural generalization of eigenmaps with L-orthonormal components. We also point out that many cla...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2016
ISSN: 0010-3640
DOI: 10.1002/cpa.21642