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UID:2213ad7f071fd237dd5c680a7cf28b58
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20230418T095754
SUMMARY: Asymptotic analysis for harmonic maps with prescribed singularities
LOCATION:SEC 208
DESCRIPTION:Abstract: Motivated by studies of axially symmetric stationary solutions of
  the Einstein vacuum equations in general relativity, we study singular har
 monic maps from the 3-dimensional Euclidean space to the hyperbolic plane, 
 with prescribed singularities. We prove that every such harmonic map has a 
 unique tangent map at the black hole horizon and the harmonic map depends o
 n the location of the black hole smoothly. The collection of parameters rep
 resenting the conical singularities in the tangent map determines a flow al
 ong which the reduced energy of the harmonic map is decreasing. The harmoni
 c map equation restricted to the unit sphere has a singularity at the north
  and south poles. The talk is based on joint work with Marcus Khuri, Gilber
 t Weinstein, and Jingang Xiong. \nSeminar website: Joint Princeton-Rutgers 
 Seminar on Geometric PDE's        \n   ( (https://sites.math.rutgers.edu/~y
 yli/joint-princeton-rutgers.html)https://sites.math.rutgers.edu/~yyli/joint
 -princeton-rutgers.html (https://sites.math.rutgers.edu/~yyli/joint-princet
 on-rutgers.html))  \n
X-ALT-DESC;FMTTYPE=text/html:<p><strong style="color: #242424; font-family: Calibri, sans-serif; font-si
 ze: 13.3333px; letter-spacing: normal; orphans: 2; text-align: start; text-
 indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spa
 cing: 0px; background-color: #ffffff;">Abstract:&nbsp;</strong>Motivated by
  studies of axially symmetric stationary solutions of the Einstein vacuum e
 quations in general relativity, we study singular harmonic maps from the 3-
 dimensional Euclidean space to the hyperbolic plane, with prescribed singul
 arities. We prove that every such harmonic map has a unique tangent map at 
 the black hole horizon and the harmonic map depends on the location of the 
 black hole smoothly. The collection of parameters representing the conical 
 singularities in the tangent map determines a flow along which the reduced 
 energy of the harmonic map is decreasing. The harmonic map equation restric
 ted to the unit sphere has a singularity at the north and south poles. The 
 talk is based on joint work with Marcus Khuri, Gilbert Weinstein, and Jinga
 ng Xiong.&nbsp;</p><p style="margin: 0in; font-size: 11pt; font-family: Cal
 ibri, sans-serif; color: #242424; font-weight: 400; letter-spacing: normal;
  orphans: 2; text-align: start; text-indent: 0px; text-transform: none; whi
 te-space: normal; widows: 2; word-spacing: 0px; background-color: #ffffff;"
 >Seminar website:&nbsp;Joint Princeton-Rutgers Seminar on Geometric PDE's&n
 bsp; &nbsp; &nbsp; &nbsp;&nbsp;</p><p style="margin: 0in; font-size: 11pt; 
 font-family: Calibri, sans-serif; color: #242424; font-weight: 400; letter-
 spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-tran
 sform: none; white-space: normal; widows: 2; word-spacing: 0px; background-
 color: #ffffff;">&nbsp;&nbsp; (<a href="https://sites.math.rutgers.edu/~yyl
 i/joint-princeton-rutgers.html" style="border: 0px; font: inherit; margin: 
 0px; padding: 0px; vertical-align: baseline; color: blue; text-decoration: 
 underline;" data-auth="NotApplicable" data-safelink="true" data-linkindex="
 0"></a><a href="https://sites.math.rutgers.edu/~yyli/joint-princeton-rutger
 s.html">https://sites.math.rutgers.edu/~yyli/joint-princeton-rutgers.html</
 a>)&nbsp;&nbsp;</p>
CONTACT:   Speaker :  Qing Han, University of Notre Dame
DTSTAMP:20260828T115744
DTSTART;TZID=America/New_York:20230421T140000
DTEND;TZID=America/New_York:20230421T150000
SEQUENCE:0
TRANSP:OPAQUE
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