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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：μ-basis for a tensor product rational surface with respect to one variable
张量积 有理曲面 变量 μ基
2023/4/28
The method of moving planes and moving quadrics expresses the implicit equation of a rational parametric surface as a compact determinant. Efficient computation of the moving planes and moving quadric...
FIRST VARIATION OF THE GENERAL CURVATURE-DEPENDENT SURFACE ENERGY
Surface energy gradient fl ow mean curvature
2015/12/11
We consider general surface energies, which are weighted integrals
over a closed surface with a weight function depending on the position, the
unit normal and the total curvature of the surface. Ene...
Formulas for the force dipole interaction of surface line defects in homoepitaxy
Formulas for the force surface line defects homoepitaxy
2015/10/16
Using asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between line defects (steps) of the same sign that form pertur...
Minimal surface systems, maximal surface systems, and special Lagrangian equations
minimal submanifold special Lagrangian equation entire solution
2012/4/17
We extend Osserman's lemma on the generalized Gauss map of two-dimensional minimal graphs of higher codimension, construct a Jenkins-Serrin type special Lagrangian Scherk graph explicitly, and general...
The Log-Convex Density Conjecture and vertical surface area in warped products
The Log-Convex Density Conjecture vertical surface area warped products Differential Geometry
2011/9/19
Abstract: We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertica...
Quillen bundle and Geometric Prequantization of Non-Abelian Vortices on a Riemann surface
Quillen bundle Geometric Prequantization Non-Abelian Vortices Riemann surface
2011/3/3
In this paper we prequantize the moduli space of non-abelian vortices.We explicitly calculate the symplectic form arising from the L2 metric and we construct a prequantum line bundle whose curvature i...
The ground state energy of a charged particle on a Riemann surface
ground state energy charged particle Riemann surface
2011/3/3
It is shown that the quantum ground state energy of particle of mass m and elec-tric charge e moving on a compact Riemann surface under the influence of a constant magnetic field of strength B is E0 =...
Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
Reconstruction of a function spherical (circular) means certain polygons and polyhedra
2010/11/26
We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). ...
We study the surface S parametrizing cuboids: it is de ned by the equations relating the sides, face diagonals and long diagonal of a rectangular box. It is an open problem whether a `rational box' ...
Parahoric bundles on a compact Riemann surface
Stable vector bundles parahoric groups parabolic bundles
2010/12/8
Let Y be a smooth projective curve (defined over the ground field C) with an action of a finite group . Let X be the smooth projective curve Y/ and let p : Y → X be the quotient mo...
Automorphisms of the Torelli complex for the one-holed genus two surface
Torelli complex one-holed genus two surface
2010/11/29
Let S be a connected, compact and orientable surface of genus two with one boundary component. We study automorphisms of the Torelli complex for S to describe any isomorphism between finite index subg...
Manin's Conjecture for a Singular Sextic del Pezzo Surface
Manin's Conjecture Singular Sextic del Pezzo Surface
2010/12/6
We prove Manin’s conjecture for a del Pezzo surface of de-gree six which has one singularity of type A2. Moreover, we achieve a meromorphic continuation and explicit expression of the associated heigh...
Using a standard fact in hyperbolic geometry, we give a simple proof of the uniqueness of PL minimal surfaces, thus filling in a gap in the original proof of Jaco and Rubinstein. Moreover, in order to...