[CvGmt News] prossimi seminari

[Giuseppe Buttazzo]

Vi ricordo dei seminari di oggi pomeriggio (Rustum Choksi alle 17.00
e Luigi De Pascale alle 18.00). I prossimi giovedi' avremo:



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Edouard Oudet (Universite' de Strasbourg + Universita' di Pisa)

"Optimization of the second Dirichlet's eigenvalue under
volume and convexity constraints."

Dipartimento di Matematica - Sala dei Seminari
Giovedi' 3 Maggio 2001 - Ore 18.00

ABSTRACT: After a short introduction on classical eigenvalues problems we
will study a question proposed by Troesh in 1973: does the stadium (the
convex hull of two tangent balls of same radius) minimize the second
Dirichlet's eigenvalue among convex domains with prescribed volume?
After the theorical study of the optimal shape we will answer to
Troesh's question and draw other consequences of the demonstration.
In a third time we will present a numerical description of the optimal shape.



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Marianna Csornyei (University College, London)

"Can one squash the space into the plane without squashing?
(Lipschitz quotient maps between finite dimensional spaces)"

Dipartimento di Matematica - Sala dei Seminari
Giovedi' 10 Maggio 2001 - Ore 18.00

Abstract:
A map $f:X\to Y$ between metric spaces $X$ and $Y$ is called a
Lipschitz quotient, if there are constants $C$, $D$ for which
$B(f(x),Dr)\subset f(B(x,r))\subset B(f(x),Cr))$ holds for every
$x\in X$ and $r>0$. The question whether a Lipschitz quotient map between
finite dimensional Euclidean spaces can increase the co-dimension of a
subspace was answered negatively in dimensions at most two. Here as a
warmup we show that for a Lipschitz quotient map $f:R^3\to R^2$ the
inverse image of a point cannot be a plane. Then we construct a
Lipschitz quotient map $f:R^3\to R^2$ for which the inverse image of
a point contains a plane.