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Dr Giuseppe Tinaglia

Education/Academic qualification

  • Doctor of Philosophy, Johns Hopkins University

    2005
  • Bachelor of Science, Università di Bologna

    2001

Research interests

My main research interest is geometric analysis with emphasis currently on the theory of minimal and constant mean curvature surfaces.<br /><br />Minimal surfaces are defined as surfaces which are critical points for the area functional. The mean curvature of a minimal surface, the average of the two principal curvatures, is identically zero. Surfaces which are critical points for the area functional under a volume constraint are instead called constant mean curvature (CMC) surfaces and in fact the average of the two principal curvatures is constant. Not only are there plenty of mathematical examples for both of these surfaces (for instance planes, helicoids and catenoids are minimal surfaces while spheres, cylinders and Delaunay surfaces are non zero CMC surfaces), but they overtly present themselves in the real world. In nature, the shape of a soap film approximates with great accuracy that of a minimal surface while soap bubbles provide the analogous approximation for CMC surfaces. In other words, a soap bubble is the least-area surface that encloses the fixed volume inside.<br />The results in my papers and my recent interests can be divided into the following areas:<br /><br /> <ul> <li>Curvature estimates for nonzero CMC disks embedded in locally homogeneous manifolds.</li> <li>The asymptotic geometric structure of nonzero CMC surfaces properly embedded in locally homogeneous manifolds.</li> <li>The rigidity of CMC surfaces immersed in locally homogeneous manifolds.</li> <li>The geometry of surfaces embedded in Euclidean space with integral bounds for the mean curvature.</li> <li>Problems and results on the number, genus, shape and other geometric properties of compact CMC surfaces from the geometry of their boundary.</li> </ul>

Participation in conference

Yorkshire and Durham Geometry Days, University of Durham

Giuseppe Tinaglia (Speaker)

Dec 2010 → …

Activity: Participating in or organising an eventParticipation in conference

The 5th KIAS Workshop on Differential Geometry, KIAS. Korea

Giuseppe Tinaglia (Speaker)

Jul 2010 → …

Activity: Participating in or organising an eventParticipation in conference

Summer School Luís Santaló 2010

Giuseppe Tinaglia (Speaker)

Jun 2010 → …

Activity: Participating in or organising an eventParticipation in conference

Geometry Day, University of Granada

Giuseppe Tinaglia (Speaker)

Dec 2009 → …

Activity: Participating in or organising an eventParticipation in conference

Minimal Surfaces, Mathematisches Forschungsinstitut Oberwolfach

Giuseppe Tinaglia (Speaker)

Oct 2009 → …

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Minimal surfaces and constant mean curvature surfaces, University of Warwick

Giuseppe Tinaglia (Speaker)

2009 → …

Activity: Participating in or organising an eventParticipation in conference

Minimal and Constant Mean Curvature Surfaces, IMPA, Brazil

Giuseppe Tinaglia (Speaker)

Aug 2007 → …

Activity: Participating in or organising an eventParticipation in conference

Southeast Geometry Seminar XI, Georgia Tech

Giuseppe Tinaglia (Speaker)

May 2007 → …

Activity: Participating in or organising an eventParticipation in conference

The 3rd Symposium on Analysis and PDEs, Purdue University

Giuseppe Tinaglia (Speaker)

May 2007 → …

Activity: Participating in or organising an eventParticipation in conference

2007 Bloomington Geometry Workshop

Giuseppe Tinaglia (Speaker)

Apr 2007 → …

Activity: Participating in or organising an eventParticipation in conference

Moduli Spaces of Properly Embedded Minimal Surfaces, AIM, Palo Alto, CA

Giuseppe Tinaglia (Speaker)

Jun 2005 → …

Activity: Participating in or organising an eventParticipation in conference

Publication peer-review

MATHEMATISCHE ZEITSCHRIFT (Journal)

Giuseppe Tinaglia (Editor)

2001 → …

Activity: Publication peer-review and editorial workPublication peer-review

BIOGERONTOLOGY (Journal)

Giuseppe Tinaglia (Editor)

2001 → …

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AMERICAN JOURNAL OF MATHEMATICS (Journal)

Giuseppe Tinaglia (Editor)

2001 → …

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Transactions of the AMS (Journal)

Giuseppe Tinaglia (Editor)

2001 → …

Activity: Publication peer-review and editorial workPublication peer-review

Proceedings of the AMS (Journal)

Giuseppe Tinaglia (Editor)

2001 → …

Activity: Publication peer-review and editorial workPublication peer-review

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