CINXE.COM

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<p>Analysis of partial differential equations (PDEs) is a very rich mathematics subject, which is broadly applied in a large variety of fields of science. It is particularly important to study nonlinear PDEs that arise in geometry and many related areas. The Geometric Partial Differential Equations Unit aims to develop new analytic methods to understand behavior of solutions to various geometric evolutions and explore solvability of nonlinear equations in general geometric settings such as sub-Riemannian manifolds and metric spaces. Our research is motivated by numerous applications in material sciences, crystal growth, image processing and is also closely connected with topics in optimal control, game theory and machine learning, etc.</p> <p>Our current research topics include the following:</p> <ul> <li>Viscosity solution theory for fully nonlinear PDEs</li> <li>Motion by curvature and more general surface evolution equations</li> <li>Convexity and other geometric properties of solutions to nonlinear PDEs</li> <li>Analysis on sub-Riemannian manifolds and general metric spaces</li> </ul> </div> </div> <aside id="sidebar-left"> <section><h3>Search this Group</h3><form class="og-search-form" action="/gpde" method="post" id="oist-solr-groups-group-search-form" accept-charset="UTF-8"><div><div class="form-item form-type-textfield form-item-search-terms"> <input type="text" id="edit-search-terms" name="search-terms" value="" size="60" maxlength="128" class="form-text" /> </div> <input type="hidden" name="group" value="32777" /> <input type="submit" id="edit-submit" name="op" value="Search" class="form-submit" /><input type="hidden" name="form_build_id" value="form-UnrQMHzKt_TuJCAgS1I-Z5LUYOEWr_GnkAHSFG4gRf8" /> <input type="hidden" name="form_id" value="oist_solr_groups_group_search_form" /> </div></form></section><section><nav id="sidebar-nav" role="navigation" class="navbar navbar-default"><ul class="nav nav-pills nav-stacked"><li class="first leaf active-trail"><a href="/gpde" target="" title="" class="active-trail active">Top</a></li> <li class="expanded"><a href="/gpde/qing-liu" target="" title="">Qing Liu</a><span class="glyphicon glyphicon-chevron-down dropdown-toggle" data-toggle="dropdown"></span><ul class="second dropdown-menu"><li class="first last leaf"><a href="https://groups.oist.jp/gpde/publications" target="" title="">Publication</a></li> </ul></li> <li class="leaf"><a href="/gpde/members" target="" title="">Members</a></li> <li class="leaf"><a href="https://groups.oist.jp/gpde/seminar-schedule" target="" title="">Seminars</a></li> <li class="expanded"><a href="https://groups.oist.jp/gpde/conferences" target="" title="">Conferences</a><span class="glyphicon glyphicon-chevron-down dropdown-toggle" data-toggle="dropdown"></span><ul class="second dropdown-menu"><li class="first leaf"><a href="https://groups.oist.jp/gpde/2025-oist-conference" target="" title="">2025 OIST Conference</a></li> <li class="leaf"><a href="https://groups.oist.jp/gpde/2024-oist-workshop" target="" title="">2024 OIST Workshop</a></li> <li class="last leaf"><a href="https://groups.oist.jp/gpde/2023-oist-meeting" target="" title="">2023 OIST Conference</a></li> </ul></li> <li class="leaf"><a href="https://groups.oist.jp/gpde/open-positions" target="" title="">Open positions</a></li> <li class="expanded"><a href="/node/32777/events" target="" title="">Upcoming Events</a><span class="glyphicon glyphicon-chevron-down dropdown-toggle" data-toggle="dropdown"></span><ul class="second dropdown-menu"><li class="first leaf"><a href="/node/32777/calendar" target="" title="">Calendar</a></li> <li class="last leaf"><a href="/node/32777/pastevents" target="" title="">Past Events</a></li> </ul></li> <li class="leaf"><a href="/gpde/posts" target="" title="">Posts</a></li> <li class="leaf"><a href="https://www.oist.jp/research/research-units/gpde/news" target="_blank" title="">OIST News Feed</a></li> <li class="last expanded"><a href="https://groups.oist.jp/gpde/annual-reports" target="" title="">Annual Reports</a><span class="glyphicon glyphicon-chevron-down dropdown-toggle" data-toggle="dropdown"></span><ul class="second dropdown-menu"><li class="first leaf"><a href="https://groups.oist.jp/gpde/fy2022-annual-report" target="" title="">FY2022</a></li> <li class="last leaf"><a href="https://groups.oist.jp/gpde/fy2023-annual-report" target="" title="">FY2023</a></li> </ul></li> </ul></nav></section><section><h3>Events</h3><div class="view view-group-events view-id-group_events view-display-id-block_1 view-dom-id-1c239c2842cb852b51406d13b83a6e25"> <ul class="events"> <li class=""> <div class="h5"><a href="/gpde/event/seminar-sharp-interface-limit-kobayashi-warren-carter-system-prof-yoshikazu-giga">[Seminar] "On a sharp interface limit of the Kobayashi-Warren-Carter system" by Prof. Yoshikazu Giga</a></div> | <span class="date-display-single">Friday, December 6, 2024 - 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