Super Stable Kählerian Horseshoe?

Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

“…(4) E extends to a continuous function on P 1 . This requires some work, see §4.6 of [4]. (5) Suppose that for some q 0 ∈ Q \ Σ the map f q0 is holomorphic, and denote this map simply by f 0 .…”

“…Theorem 1 shows that E(f q ) is a subharmonic function on Q \ Σ. To illustrate how this can be put to work, we discuss a special case of results in §4.6 of [4]. Namely, if the V q form a Lefschetz pencil and if one f q is holomorphic, then f is holomorphic.…”

L-cut splitting of translation surfaces and non-embedding of pseudo-Anosovs (in genus two)

“…Anosov map has orientable stable/unstable foliations then the embedding has to coincide with the map h : M → T N given by the very general π 1 -stability theorem of Franks [12], first invoked in this context by Fathi [11]. (In the recent survey [14], Gromov calls h Abel-Franks map, after drawing a parallel with the classical Abel-Jacobi embedding of a Riemann surface. )…”

“…The first fact is that one may well assume that ψ induced map on homologies, ψ * : R), is surjective. To be precise, consider the image The second item is the uniqueness of ψ, which goes back to Franks [12] and is considered in a much broader context in Gromov [14].…”

Hilbert Volume in Metric Spaces

“…Besides f ◇ , there is also a dynamical counterpart to the Abel-Jacobi-Albanese, called the Shub-Franks map that is associated with hyperbolic endomorphisms of tori and infra-nil-manifolds in general. The three maps and their generalizations intricately intertwine in their applications to the geometric rigidity theory (See [15] for a related discussion on A-J-A -S-F connection. )…”