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# Matematiska kollokviet

Organiserat av Anders Björn, Milagros Izquierdo, Vladimir Kozlov och Hans Lundmark.

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## Onsdag 3 maj 2017, David Rule, MAI

Seminariet är ett samarrangemang med Tvärvetenskapliga seminariet.

Talare: David Rule, MAI

Titel: The global boundedness of Fourier integral operators on local Hardy spaces

Tid och plats: Onsdag 3 maj 2017, Hopningspunkten, 13.15–14.15

Sammanfattning: The question of the local $L^p$-boundedness of Fourier integral operators when $p\neq2$ was answered in work of Seeger-Sogge-Stein in the early nineties. But only recently have Ruzhansky-Sugimoto found sufficient conditions to prove global $L^p$-boundedness. We build on their methods to prove the global boundedness of Fourier integral operators in the (mostly quasi-Banach) setting of local Hardy spaces $h^p$ in the range $n/(n+1) < p \leq 1$. This is joint work with Salvador Rodríguez-López and Wolfgang Staubach.

## Onsdag 10 maj 2017, Nageswari Shanmugalingam, MAI

Talare: Nageswari Shanmugalingam, MAI

Titel: Notions of quasiconformality in non-smooth setting

Tid och plats: Onsdag 10 maj 2017, Hopningspunkten, 13.15–14.15

Sammanfattning:  The aim of this talk is to give an overview of different notions of quasiconformality that are equivalent in the Euclidean setting, and the relationships between them under certain geometric assumptions on the non-smooth metric measure spaces.

## Onsdag 17 maj 2017, Oscar Perdomo, Central Connecticut State University, New Britain, CT, USA

Talare: Oscar Perdomo, Central Connecticut State University, New Britain, CT, USA

Titel: Embedded constant mean curvature hypersurfaces on spheres

Tid och plats: Onsdag 17 maj 2017, Hopningspunkten, 13.15–14.15

Sammanfattning: In this talk we will discuss hypersurfaces of the $(n+1)$-dimensional unit sphere with exactly two principal curvatures and constant mean curvature -cmc-.  Besides providing an explicit construction for these hypersurfaces, we will show that for every positive integer $m>1$ and any $H$ between $\cot(\pi/m)$ and $b_{mn} = (m^2-2)((n-1)/(n^2(m^2-1))^{1/2}$, there exists an embedded hypersurface with cmc $H$ and with group of isometries invariant under the cyclic group $Z_m$. When $H$ is close to $\cot(\pi/m)$, the hypersurface looks like a necklace made out of $m$ spheres and $m+1$ catenoid necks attached. When H is close to $b_{mn}$, the hypersuface looks like the cartesian product of an $(n-1)$-dimensional sphere with a circumference. Several images of these examples will be shown.

When $n=2$, this is, for surfaces in the three dimensional sphere, we have that for every $H$ between $\cot(\pi/m)$ and $(m^2-2)/2(m^2-1)^{1/2}$, there exists an embedded surface with cmc $H$.  Andrews and Li showed that these surfaces are the only embedded tori in the sphere with cmc. We will finish the talk by doing some comments on Andrews and Li’s proof.

Sidansvarig: milagros.izquierdo@liu.se
Senast uppdaterad: Mon Apr 03 15:00:42 CEST 2017