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We describe a family of calibrations arising naturally on a hyperk¨ahler manifoldM. These calibrations calibrate the holomorphic Lagrangian,holomorphic isotropic and holomorphic coisotropic subvarieti...
We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free b...
Representation stacks, D-branes and noncommutative geometry
Representation stacks D-branes noncommutative geometry
2010/12/13
n this note we prove that the spec(C)-points of the representation Artin-stack [repnR/PGLn] of n-dimensional representations of an affine C-algebra R correspond to C-algebra morphisms R - An where An ...
In this note, we introduce a class of cell decompositions of PL manifolds and polyhedra which are more general than triangulations yet not as general as CW complexes; we propose calling them PLCW comp...
Resonance equals reducibility for A-hypergeometric systems
toric hypergeometric Euler–Koszul homology D-module resonant
2010/12/8
Classical Theorems of Gel’fand et al., and recent results of Beuk-ers show essentially that non-confluent A-hypergeometric systems have re-ducible monodromy representation if and only if the continuou...
We use basic results from shape theory to investigate inverse systems of covers and the corresponding fundamental pro-groups. Many of the standard shape-theoretic definitions become simpler in the con...
A theorem of Lawson and Simons states that the only stable minimal submanifolds in CPn are complex submanifolds. We generalize their result to the cases of HPn and OP2. Our approach gives a unified vi...
Automorphisms of the Torelli complex for the one-holed genus two surface
Torelli complex one-holed genus two surface
2010/11/29
Let S be a connected, compact and orientable surface of genus two with one boundary component. We study automorphisms of the Torelli complex for S to describe any isomorphism between finite index subg...
Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity
Kleinian groups Poincar´ e exponent fractal geometry dissipative dy-namics
2010/11/29
The main result of this paper is to show that if N is a normal subgroup of a Kleinian group G such that G/N contains a coset which is represented by some loxodromic element, then the Hausdorff dimensi...
The caloric gauge was introduced in [24] by Tao with studying large data energy critical wave maps mapping from R2+1 to hyperbolic space Hm in view.
A conjugation-free geometric presentation of fundamental groups of arrangements II: Expansion and some properties
conjugation-free geometric presentation of fundamental groups some properties
2010/12/1
A conjugation-free geometric presentation of a funda-mental group is a presentation with the natural topological gener-ators x1, . . . , xn and the cyclic relations.
Generalized Newton's Method based on Graphical Derivatives
nonsmooth equations optimization and variational analysis Newton’s method
2010/11/29
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify
a new generalized Newt...
We establish a classification of cubic minimal cones in case of the so-called radial
eigencubics. Our principal result states that any radial eigencubic is either a member of the
infinite family of ...
On the existence of non-abelian monopoles: the algebro-geometric approach
existence of non-abelian monopoles algebro-geometric approach
2010/12/9
We develop the Atiyah-Drinfeld-Manin-Hitchin-Nahm construction to study SU(2) non-abelian charge 3 monopoles within the algebro-geometric method. The method starts with nding an algebraic curve, the ...
Géométries relatives (Relative geometries)
Model Theory Amalgamation methods CM-triviality Geometry,Group Definability
2010/11/29
R´esum´e. Une analyse des propri´et´es g´eom´etriques d’une structure relatives `a un reduit est entam´ee. En particulier la d´efinissabilit´e des...