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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Kazdan-Warner equations on compact Riemann surfaces
紧黎曼曲面 卡兹丹-华纳方程 数学
2023/4/28
In this talk, we shall review firstly the study history of Kazdan-Warner equations on compact Riemann surfaces, which was proposed by Kazdan and Warner on Annals of Math on 1974. Then we shall show th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent developments on random hyperbolic surfaces of large genus
大属随机 双曲曲面 球面几何
2023/4/21
In this talk, we report several very recent asymptotic results on certain classical geometric quantities viewed as random variables on the moduli space of Riemann surfaces for large genus (and many cu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Kahler Ricci shrinker surfaces
Kahler Ricci 收缩机 表面
2023/4/23
We prove that any K?hler Ricci shrinker surface has bounded sectional curvature. Combining this estimate with earlier work by many authors, we provide a complete classification of all K?hler Ricci shr...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements II: tilted interlacements and solidification of porous surfaces
随机交错 大偏差 倾斜交错 多孔表面 固化
2023/5/10
In this lecture, I will discuss how tilting and coarse graining, two key ideas in modern probability, come into play in deriving respectively the lower and upper bounds of the asymptotic probability i...
中国地质大学科学技术发展院左博新，胡祥云*等，计算机学院，Geophysical Research Letters （2020），Downward Continuation and Transformation of Total‐Field Magnetic Anomalies Into Magnetic Gradient Tensors Between Arbitrary Surfaces Using Multilayer Equivalent Sources
资源勘探；等效源方法；磁测；数据；下延拓；磁梯度；张量；转换计算
2021/10/15
近日，地球物理著名期刊《Geophysical Research Letters》正式刊发了中国地质大学胡祥云教授团队研究成果 -“Downward continuation and transformation of total-field magnetic anomalies into magnetic gradient tensors between arbitrary surfaces u...
ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
Riemann surface fundamental group flat bundle harmonic map energy Teichmuller space convex cocompact hyperbolic manifold
2015/12/17
The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichm¨uller space TS which is a qualitative invariant of the ...
Precise Constants in Bosonization Formulas on Riemann Surfaces. I
Bosonization Formulas Riemann Surfaces
2015/12/17
A computation of the constant appearing in the spin-1 bosonization formulais given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with res...
GLUING FORMULAS FOR DETERMINANTS OF DOLBEAULT LAPLACIANS ON RIEMANN SURFACES
Determinants of Laplace operators Riemann surfaces bosonization formulas
2015/12/17
We present gluing formulas for zeta regularized determinants of Dolbeault laplacians on Riemann surfaces. These are expressed in terms of determinants of associated operators on surfaces with boundary...
On the blow-up set of the Yang–Mills flow on Kahler surfaces
blow-up set Yang–Mills flow Kahler surfaces
2015/12/17
The Yang–Mills flow on a Kahler surface with holomorphic initial data converges smoothly away from a singular set determined by the Harder–Narasimhan–Seshadri filtration of the initial holomorphic bun...
The study of the spectrum of the Laplace operator has produced an extensive literature. (See [Cha] and the references therein.) Of special interest to recent applications has been the behavior of spec...
Unification of step bunching phenomena on vicinal surfaces
step bunching phenomena vicinal surfaces
2015/10/16
We unify step bunching SB instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting p...
Homogenization of reconstructed crystal surfaces:Fick’s law of diffusion
Homogenization reconstructed crystal surfaces Fick’s law of diffusion
2015/10/16
Fick’s law for the diffusion of adsorbed atoms adatoms on crystal surfaces below roughening is generalized to account for surface reconstruction. In this case, material parameters vary spatially at ...
One-dimensional model of interacting-step fluctuations on vicinal surfaces:Analytical formulas and kinetic Monte Carlo simulations
One-dimensional model interacting-step fluctuations vicinal surfaces Analytical formulas kinetic Monte Carlo simulations
2015/10/16
We study analytically and numerically a one-dimensional model of interacting line defects steps fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for appr...
CONNECTION OF KINETIC MONTE CARLO MODEL FOR SURFACES TO ONE-STEP FLOW THEORY IN 1+1 DIMENSIONS
kinetic Monte Carlo Burton–Cabrera–Frank theory low-density approximation near-equilibrium condition master equation maximum principle
2015/10/16
The Burton–Cabrera–Frank (BCF) theory of step flow has been recognized as a valuable tool for describing nanoscale evolution of crystal surfaces. We formally derive a single-step BCF-type model from a...