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You searched for `+publisher:"University of Notre Dame" +contributor:("Fred Xavier, Committee Member")`

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University of Notre Dame

1. Xiaoyang Chen. Curvature and Riemannian Submersions</h1>.

Degree: Mathematics, 2014, University of Notre Dame

URL: https://curate.nd.edu/show/fb494744f2q

We study Riemannian submersions from
positively curved manifolds and from Einstein manifolds. We first
prove a diameter rigidity theorem for Riemannian
submersions.Secondly we show that there is no nontrivial Riemannian
submersion from positively curved four manifolds such that either
the mean curvature vector field or the norm of the O'Neill tensor
is basic. We also classify Riemannian submersions from compact
four-dimensional Einstein manifolds with totally geodesic
fibers.
*Advisors/Committee Members: Karsten Grove, Committee Chair, Stephan Stolz, Committee Member, Fred Xavier, Committee Member, Xiaobo Liu, Committee Member.*

Subjects/Keywords: Fred Wilhelm’s conjecture; Riemannian submersions

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Chen, X. (2014). Curvature and Riemannian Submersions</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/fb494744f2q

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Chen, Xiaoyang. “Curvature and Riemannian Submersions</h1>.” 2014. Thesis, University of Notre Dame. Accessed November 28, 2020. https://curate.nd.edu/show/fb494744f2q.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Chen, Xiaoyang. “Curvature and Riemannian Submersions</h1>.” 2014. Web. 28 Nov 2020.

Vancouver:

Chen X. Curvature and Riemannian Submersions</h1>. [Internet] [Thesis]. University of Notre Dame; 2014. [cited 2020 Nov 28]. Available from: https://curate.nd.edu/show/fb494744f2q.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chen X. Curvature and Riemannian Submersions</h1>. [Thesis]. University of Notre Dame; 2014. Available from: https://curate.nd.edu/show/fb494744f2q

Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

2. Jian Ge. Low Dimension Soul Theorems</h1>.

Degree: Mathematics, 2011, University of Notre Dame

URL: https://curate.nd.edu/show/kd17cr58x0q

We study the Soul theorem for low dimensional
topologically regular open complete nonnegatively curved Alexandrov
spaces and give a topological classification of these spaces. These
spaces occurs naturally as the blow-up limits of sequences of
Riemannian manifold with a lower curvature bound. This will be used
to study the collapsing of 3-dimension manifold as well as of
4-dimension Riemannian manifold with a lower curvature bound. These
spaces have also been studied in [SY00] and [Yam02]. Our main tools
are critical point theory for distance functions and Perelman’s
Fibration Theorem.
*Advisors/Committee Members: Brian Smyth, Committee Member, Jianguo Cao, Committee Chair, Karsten Grove, Committee Member, Fred Xavier, Committee Member.*

Subjects/Keywords: Soul theorem; Alexandrov geometry

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Ge, J. (2011). Low Dimension Soul Theorems</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/kd17cr58x0q

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Ge, Jian. “Low Dimension Soul Theorems</h1>.” 2011. Thesis, University of Notre Dame. Accessed November 28, 2020. https://curate.nd.edu/show/kd17cr58x0q.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Ge, Jian. “Low Dimension Soul Theorems</h1>.” 2011. Web. 28 Nov 2020.

Vancouver:

Ge J. Low Dimension Soul Theorems</h1>. [Internet] [Thesis]. University of Notre Dame; 2011. [cited 2020 Nov 28]. Available from: https://curate.nd.edu/show/kd17cr58x0q.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ge J. Low Dimension Soul Theorems</h1>. [Thesis]. University of Notre Dame; 2011. Available from: https://curate.nd.edu/show/kd17cr58x0q

Not specified: Masters Thesis or Doctoral Dissertation

University of Notre Dame

3. Sujin Khomrutai. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.

Degree: Mathematics, 2009, University of Notre Dame

URL: https://curate.nd.edu/show/wd375t37b4z

We prove some regularity results for singular
solutions of σ_{k}-Yamabe problem, where the singular set is a
compact hypersurface in a Riemannian manifold. This problem is a
fully nonlinear version of the singular Yamabe problem, which is an
equation of semilinear type. Apart from their importance in
conformal geometry, the blow-up solutions along a hypersurface or
the boundary of a manifold have also received much attention in the
study of AdS/CFT correspondence in physics. We study the problem in
the case of negative cone. In this case, the main difficulty is the
lack of C^{2} estimate, so we have to rely on the maximum principle
and method of sub- and super-solutions. Combining our result with
the theory of “Edge Differential Operators” developed by R. Mazzeo
we obtain a polyhomogeneous expansion of any singular solutions in
terms of the distance to the singular set.
*Advisors/Committee Members: Fred Xavier, Committee Member, Alex Himonas, Committee Member, Matthew Gursky, Committee Chair, Robert Rennie, Committee Member, Brian Smyth, Committee Member.*

Subjects/Keywords: singular solutions; partial differential equation

Record Details Similar Records

❌

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Khomrutai, S. (2009). Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/wd375t37b4z

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Khomrutai, Sujin. “Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.” 2009. Thesis, University of Notre Dame. Accessed November 28, 2020. https://curate.nd.edu/show/wd375t37b4z.

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Khomrutai, Sujin. “Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>.” 2009. Web. 28 Nov 2020.

Vancouver:

Khomrutai S. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. [Internet] [Thesis]. University of Notre Dame; 2009. [cited 2020 Nov 28]. Available from: https://curate.nd.edu/show/wd375t37b4z.

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Khomrutai S. Regularity of Singular Solutions to Sigma_k-Yamabe Problems</h1>. [Thesis]. University of Notre Dame; 2009. Available from: https://curate.nd.edu/show/wd375t37b4z

Not specified: Masters Thesis or Doctoral Dissertation