Name: Ettore Minguzzi
Position: Associate Professor MAT/07-Mathematical Physics (with 2012 Italian full professor qualification) at
Università degli Studi
Dipartimento di Matematica e Informatica "U. Dini",
Via S. Marta 3,
I-50139 Firenze, Italia
Tel. +39 055 2758 925
Fax. +39 055 471787
My pgp key
relativity, global Lorentzian and Lorentz-Finsler geometry, topological preordered spaces.
you do not see the navigation bar click here.
NEWS: International Meeting on Non-regular spacetime geometry
(for references email me or check my publication list)
Mathematical Relativity and topological ordered spaces:
- Definition and development of affine sphere spacetimes
- Positive solution of an old conjecture concerning
of compact Cauchy horizons under positive energy conditions. Consequent
results on the fact that under reasonable conditions Lorentzian
cobordisms are trivial (no topology change), and closed timelike curves
cannot form (no time machines). Proof that Cauchy horizons with compact
components cannot form from reasonable initial data (a case of strong
cosmic censorship conjecture).
- Strengthening of Hawking's area theorem for horizons.
- Proof that convex normal globally hyperbolic
- Extension of singularity theorems to the Finsler case.
- Proof that causality theory can be generalized to the Finslerian
case and/or to the Lipschitz connection case, extending proofs word by word
(whenever curvature is not involved).
- Proof of the reverse Cauchy-Schwarz and reverse triangle
inequality for Lorentz-Finsler geometry with metric defined on the
slit tangent bundle or on conic subbundles.
- Proof that the Lorentz-Finsler theory for metrics defined on the
slit tangent bundle predicts two lightlike cones as desired provided
the spacetime dimension is larger than two.
- Proof that locally Lipschitz and anti-Lipschitz time functions
can be approximated by smooth time functions with timelike gradient.
Also Hawking's time function can be so approximated.
- Proof of the stability of global hyperbolicity.
- Proof that any topological preordered space endowed with a closed
order determined by local data (e.g. cone structure) in which the
topology is sufficiently good is quasi-uniformizable, namely topology
and order can be recovered from the sets of isotone (non-decreasing)
functions. Thus these spaces admit a Nachbin compactification.
- Proof that stably causal spacetimes are quasi-uniformizable (the
causal order and the topology follow from the set of time
functions) and that globally hyperbolic spacetimes are even
quasi-pseudo-metrizable. Thus stably casusal spacetimes can be
- Proof that every closed preordered space endowed with a locally
compact sigma-compact topology is normally preordered. Under second
countability it admits a countable utility representation.
- Realization that there is a nice relationship between economics
results on utility theory and relativistic results on time functions.
- Proof of a novel type of singularity theorem which states that
under standard genericity and positive energy conditions either the
spacetime admits a time function or it has pathologies in the form
of chronology violation or lightlike geodesic singularities.
- Positive solution of Low's conjecture on the equivalence between
Sorkin and Woolgar's K-causality and Hawking's stable causality.
- Clarification of the causal ladder, e.g. through the introduction of the non-imprisonment conditions.
- Development of limit curve theorems without casuality conditions.
- Proposal that the Big Bang is a lightlike boundary of a
chronology violating set. This model nicely solves the
homogenity/isotropy and entropy problems of cosmology.
- Extension of the Avez-Seifert geodesic connectedness theorem to the Lorentz force case.
- Classification of the conjugacy classes of the
inhomogeneous Lorentz group and proof of a relativistic Chasles
- Proof that the exponential map for Lipschitz connections or
sprays is strongly differentiable at the origin and provides a local
- Introduction of a third order equation alternative to the Lagrange equation and introduction of the Power Lagrangian.
- Clarification of simultaneity issues using the concept of round-trip time and proposal of alternative synchronization schemes.