<div dir="ltr"><p class="" style="text-align:center"><span style="font-size:18pt;font-family:'Times New Roman',serif">SEMINARIO
DI MATEMATICA</span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Mercoledì 2 dicembre 2015</span><span style="font-size:16pt;font-family:'Times New Roman',serif"></span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">ore 15:00</span></p>

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<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><u><span style="font-size:16pt;font-family:'Times New Roman',serif">Scuola Normale Superiore</span></u></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Pisa</span></p>

<p class="MsoNormal" align="center" style="margin-left:9pt;text-align:center;line-height:18pt"><span style="font-size:16pt;font-family:'Times New Roman',serif">Aula Mancini</span></p>

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<pre style="text-align:center"><b><span style="font-size:22pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">Monica Musso </span></b></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial">(PUC)</span><b></b></i></pre><pre style="text-align:center"><i><span style="font-size:12pt;font-family:'Times New Roman',serif;background-image:initial;background-repeat:initial"> </span></i></pre>

<p class="MsoNormal" align="center" style="text-align:center"><span style="font-size:16pt;font-family:'Times New Roman',serif">Terrà un
seminario dal titolo:</span></p>

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<p class="MsoNormal" align="center" style="text-align:center"><b><span lang="EN-US" style="font-size:22pt;font-family:'Times New Roman',serif">“<span style="background-image:initial;background-repeat:initial">A
non-compactness result on the fractional Yamabe problem in large dimensions</span></span>”</b></p>

<p class="MsoNormal" align="center" style="text-align:center"><b><span lang="EN-US" style="font-size:22pt;font-family:'Times New Roman',serif"> </span></b></p>

<p class="MsoNormal" style="text-align:justify"><b><span lang="EN-US" style="font-family:'Times New Roman',serif">Abstract:</span></b></p>

<p class=""><font face="arial, helvetica, sans-serif"><i><span lang="EN-GB" style="background-image:initial;background-repeat:initial">Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional
asymptotically hyperbolic manifold with a conformal infinity $(M^n, [h])$.</span></i><i><span lang="EN-GB"> <span style="background-image:initial;background-repeat:initial">The fractional Yamabe problem
addresses to solve</span></span> <span style="background-image:initial;background-repeat:initial">\[P^{\gamma}[g^+,h]
(u) = cu^{n+2\gamma \over n-2\gamma}, \quad u > 0 \quad \text{on } M\]</span>
<span style="background-image:initial;background-repeat:initial">where $c \in {\mathbb{R} $ and
$P^{\gamma}[g^+,h]$ is the fractional conformal Laplacian whose principal
symbol is $(-\Delta)^{\gamma}$.</span> <span style="background-image:initial;background-repeat:initial">We
construct a metric on the half space $X = {\mathbb{R}^{n+1}_+$, which is
conformally equivalent to the unit ball,</span> <span style="background-image:initial;background-repeat:initial">for which the solution set of the fractional Yamabe equation is
non-compact</span> <span style="background-image:initial;background-repeat:initial">provided that $n \ge
24$ for $\gamma \in (0, \gamma^*)$ and $n \ge 25$ for $\gamma \in [\gamma^*,1)$
where $\gamma^* \in (0, 1)$ is a certain transition exponent.</span> <span style="background-image:initial;background-repeat:initial">The value of $\gamma^*$ turns out to be approximately
0.940197. This is a joint work with Seunghyeok Kim and Juncheng Wei.</span></i><i><span lang="EN-US"></span></i></font></p>

<p class=""><i><span lang="EN-US"><font face="arial, helvetica, sans-serif"> </font></span></i></p>

<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif">Tutti gli
interessati sono invitati a partecipare.</span></p>

<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif"> </span></p>

<p class=""><span style="font-size:16pt;font-family:'Times New Roman',serif">Classe di Scienze
Matematiche e Naturali</span></p>

<p class=""><br></p><div><div class="gmail_signature"><div dir="ltr"><div>Valeria Giuliani</div><div>Scuola Normale Superiore</div><div>Servizio alla Didattica e Allievi</div><div>tel. 050 509260</div><div>Piazza dei Cavalieri, 7</div><div>56126 Pisa</div><div>E-mail: <a href="mailto:valeria.giuliani@sns.it" target="_blank">valeria.giuliani@sns.it</a></div><div>E-mail: <a href="mailto:classi@sns.it" target="_blank">classi@sns.it</a></div></div></div></div>
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