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In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
The constant rank theorem was initially developed by Caffarelli-Friedman in 1985 in two-dimensions for convex solutions of semilinear equations. Later, Korevaar-Lewis extended the result to higher dim...
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...
THE LOOPING CONSTANT OF Zd     LOOPING CONSTANT  Zd       2015/8/14
The looping constant ξ(Zd) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Zd.Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilso...
We consider a control system in which sensor data is transmitted from the plant to a receiver over a communication channel, and the receiver uses the data to estimate the state of the plant. Using a f...
We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1 Laplacian ∆1 . The eigenvalue problem is to solve a nonlinear system, involving a set valued f...
In this paper we are concerned with substructuring methods for the second-order elliptic problems in three-dimensional domains. We 痳st design a simple and completely explicit nearly harmonic extensi...
Considering multivariate strongly mixing time series, nonparametric tests for a constant copula with specified or unspecified change point (candidate) are derived; the tests are consistent against gen...
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the ...
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their construction...

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