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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...
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 ...
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...
Crooked planes were defined by Drumm to bound fundamental polyhedra in Minkowski space for Margulis spacetimes.
They were extended by Frances to closed polyhedral surfaces in the
conformal com...
AFFINE CUBIC SURFACES AND RELATIVE SL(2)-CHARACTER VARIETIES OF COMPACT SURFACES
AFFINE CUBIC SURFACES RELATIVE SL(2)-CHARACTER
2015/9/29
A natural family of affine cubic surfaces arises from
SL(2)-characters of the 4-holed sphere and the 1-holed torus. The
ideal locus is a tritangent plane which is generic in the sense that
the...
CONVEX REAL PROJECTIVE STRUCTURES ON CLOSED SURFACES ARE CLOSED
REAL PROJECTIVE STRUCTURES CLOSED SURFACES
2015/9/29
T. The deformation space t(E) of convex Rp2_ structures on a closed
surface Y with X(z) < 0 is closed in the space Hom(7r, SL(3, IR))/SL(3, IR)
of equivalence classes of representations r1 (l) -- ...
A symplectic structure on a manifold is a closed nondegenerate exterior 2-
form. The most common type of symplectic structure arises on a complex
manifold as the imaginary part of a Hermitian metr...
Averaging of incompressible flows on two-dimensional surfaces
Averaging Markov Process Incompressible Flow Gluing Conditions Diffusion on a Graph
2015/9/25
We consider a process on a compact two-dimensional surface which consists of the fast motion along the stream lines of an incompressible periodic vector field perturbed by white noise. It gives rise t...
A Simple Manifold-Based Construction of Surfaces of Arbitrary Smoothness
Geometric modeling manifolds
2015/7/14
We present a smooth surface construction based on the manifold approach of Grimm and Hughes. We demonstrate how this approach can relatively easily produce a number of desirable properties which are h...
Enumerative Geometry on Enriques surfaces.
Ricci surfaces
minimal surfaces Ricci condition generalized Killing spinors Ricci surfaces
2012/6/29
A Ricci surface is a Riemannian 2-manifold $(M,g)$ whose Gaussian curvature $K$ satisfies $K\Delta K+g(dK,dK)+4K^3=0$. Every minimal surface isometrically embedded in $\mathbb{R}^3$ is a Ricci surface...
We characterize helix surfaces in the Berger sphere. In particular, we prove that, locally, a helix surface is invariant by the action of a 1-parameter group of isometries of the ambient space.
Some properties of Holder surfaces in the Heisenberg group
properties of Holder surfaces Heisenberg group Differential Geometry
2012/5/9
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into ...
Dyck's surfaces, systoles, and capacities
Systole optimal systolic inequality extremal metric nonpositively curved surface Riemann surface
2012/5/9
We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle 9?pi - theta, for a...