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Our motivation for studying this problem is threefold:
(i) When one fixes r = m = 0, the resulting two parameter family is a normal
form for a codimension two bifurcation within the class of planar ...
Effective vanishing theorems for ample and globally generated vector bundles
Effective vanishing theorems ample globally generated vector bundles
2018/4/19
By proving an integral formula of the curvature tensor of E⊗detE, we observe that the curvature of E⊗detE is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Na...
Difference bodies in complex vector spaces
Difference bodies complex vector spaces Differential Geometry
2012/6/21
A complete classification is obtained of continuous, translation invariant, Minkowski valuations on an m-dimensional complex vector space which are covariant under the complex special linear group.
This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We study its v...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
A geometric heat flow for vector fields
Geometric heat flow Killing vector fields Yano’s theorem Navier-Stokes equations
2011/9/6
Abstract: This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We s...
On vector fields having properties of Reeb fields
Reeb field presymplectic form contact form geodesible field
2011/9/5
Abstract: We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional mani...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
A Simple Vector Proof of Feuerbach's Theorem
Simple Vector Proof Feuerbach's Theorem Metric Geometry
2011/8/26
Abstract: The celebrated theorem of Feuerbach states that the nine-point circle of a nonequilateral triangle is tangent to both its incircle and its three excircles. In this note, we give a simple pro...
Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds, II
Riemannian Manifolds Killing vector fields Rellich identities
2011/1/21
We propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds ad...
Modification of the Simpson moduli space M_{3m+1}(P_2) by vector bundles (I)
Modification Simpson moduli space M_{3m+1}(P_2) vector bundles (I)
2011/2/28
We consider the moduli space of stable vector bundles on curves embedded in P2 with Hilbert polynomial 3m+ 1 and construct a compactification of this space by vector bundles. The result fM is a blow u...
n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization
n-Channel Asymmetric Entropy-Constrained Lattice Vector Quantization
2011/1/14
This paper is about the design and analysis of an index-assignment (IA) based multiple-description coding scheme for the n-channel asymmetric case.
Vector bundles of rank 2 computing Clifford indices
Semistable vector bundle Clifford indices gonality
2011/1/17
Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices.
This is of pa...
Convergence of distributed asynchronous learning vector quantization algorithms
Convergence of distributed asynchronous vector quantization algorithms
2011/2/25
Motivated by the problem of effectively executing clustering algo-rithms on very large data sets, we address a model for large scale dis-tributed clustering methods.
CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities
CMB Bispectrum Primordial Scalar Vector Tensor non-Gaussianities
2011/3/2
We present an all-sky formalism for the CMB bispectrum induced by the primordial non-Gaussianities not only in scalar but also in vector and tensor fluctuations. We find that the bispectrum can be for...