We study the natural compactification of the moduli space of branched minimal immersions of S into S. We prove that the (compactified) moduli space Md is a connected projective variety of dimension 2d+ 4. It is irreducible when d = 1, 2, and it has two irreducible components when d ≥ 3. We discuss the bubbling phenomenon at the boundary of the moduli space.

We study the properties of certain affine invariant measures of symmetry associated to a compact convex body L in a Euclidean vector space. As functions of the interior of L, these measures of symmetry are proved or disproved to be concave in specific situations, notably for the reduced moduli of spherical minimal immersions. MSC 2000: 53C42

A spectral sequence which may be regarded as an 'Adams spectral sequence over a fixed space 2?' has been constructed by J. F. McClendon [6] and J.-P. Meyer [8]. This note describes a generalization in which there is no need for any orientability assumptions. The construction is carried out in a suitable stable category, which may be of independent interest. An application to the enumeration of ...

A two-dimensional string model with dynamical cancellation of folds is considered. The action of the model contains the self-intersection number which is defined for surfaces immersed into 4D targets. The two additional variables are not dynamical and live on a compact manifold. In this sense the model is a compactification of a 4D theory. The cancellation forces the string θ angle to be equal ...

The space B i = Imm(S,R)/Diff(S) of all immersions of rotation degree 0 in the plane modulo reparametrizations has homotopy groups π1(B i ) = Z, π2(B 0 i ) = Z, and πk(B 0 i ) = 0 for k ≥ 3.

We prove an existence result for local and global G-structure preserving affine immersions between affine manifolds. Several examples are discussed in the context of Riemannian and semi-Riemannian geometry, including the case of isometric immersions into Lie groups endowed with a left-invariant metric, and the case of isometric immersions into products of space forms.

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two subbundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either b...