Harmonic diffeomorphisms between the annuli with rotational symmetry
Dienstag, 28.10.14, 16:00-17:00, Raum 404, Eckerstr. 1
We give some necessary and sufficient conditions for the existence of rotationally symmetric harmonic diffeomorphism between the annuli with the hyperbolic metric, Poincaré metric, or Euclidean metric on the target respectively.\n
Discrete quasi-Einstein metrics and combinatorial curvature flows in
Dienstag, 4.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Motivated by the definition of combinatorial scalar curvature given by Cooper and Rivin, we introduce a \nnew combinatorial scalar curvature. Then we define \nthe discrete quasi-Einstein metric, which is a combinatorial analogue of the constant scalar curvature metric in smooth case. We find that discrete quasi-Einstein metric is critical point of both the combinatorial Yamabe functional and the quadratic energy functional we defined on triangulated 3-manifolds. We introduce combinatorial curvature flows, including a new type of combinatorial Yamabe flow, to study the discrete quasi-Einstein metrics and prove that the flows produce solutions converging to discrete quasi-Einstein metrics if the initial normalized quadratic energy is small enough. As a corollary, we prove that nonsingular solution of the combinatorial Yamabe flow with nonpositive initial curvatures converges to discrete quasi-Einstein metric. The proof relies on a careful analysis of the discrete dual-Laplacian, which we interpret as the Jacobian matrix of curvature map.
The Ricci Flow on Surfaces
Dienstag, 11.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Differntial Harnack inequality along the Ricci flow
Dienstag, 18.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
Bochner-Weitzenboeck formula and Harnack estimates for Finsler manifolds
Dienstag, 25.11.14, 16:00-17:00, Raum 404, Eckerstr. 1
The Existence of Hermitian-Yang-Mills connection over compact Kähler manifold
Dienstag, 2.12.14, 16:00-17:00, Raum 404, Eckerstr. 1
Some Aspects of the Dynamic of V=H−H
Dienstag, 20.1.15, 16:00-17:00, Raum 404, Eckerstr. 1
We consider the evolution of a surface Γ(t) according to the equation V=H−H, where V is the normal velocity of Γ(t), H is the sum of the two principal curvatures and H is the average of H on Γ(t). We study the case where Γ(t) intersects orthogonally a fixed surface Σ and discuss some aspects of the dynamics of Γ(t) under the assumption that the volume of the region enclosed between Γ(t) and Σ is small. We show that, in this case, if Γ(0) is near a hemisphere, Γ(t) keeps its almost hemispherical shape and slides on Σ crawling approximately along orbits of the tangential gradient ∇HΣ of the sum HΣ of the two principal curvatures of Σ. We also show that, if p∈Σ is a nondegenerate zero of ∇HΣ and a>0 is sufficiently small, then there is a surface of constant mean curvature which is near a hemisphere of radius a with center near p and intersects Σ orthogonally.
Anti-Self-Dual Yang-Mills connections on stable bundles over albebraic surfaces
Dienstag, 3.2.15, 16:00-17:00, Raum 404, Eckerstr. 1
We will have a carefull study about sir Donaldson´s paper "Anti-Self-Dual Yang-Mills connections over Algebraic surfaces and stable vector bundles",which gives a proof about the 2 dimensional case of Hitchin-Kobayashi correspondence,by the techniques of choosing good gauge to obtain the the convergence of connections under Yang Mills flow to Hermitian-Yang-Mills connection.