Concentration of small Hawking type surfaces

Research output: Contribution to journal › Journal article › Research › peer-review

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Concentration of small Hawking type surfaces. / Friedrich, Alexander.

In: Differential Geometry and its Application, Vol. 85, 101927, 2022, p. 1-23.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Friedrich, A 2022, 'Concentration of small Hawking type surfaces', Differential Geometry and its Application, vol. 85, 101927, pp. 1-23. https://doi.org/10.1016/j.difgeo.2022.101927

APA

Friedrich, A. (2022). Concentration of small Hawking type surfaces. Differential Geometry and its Application, 85, 1-23. [101927]. https://doi.org/10.1016/j.difgeo.2022.101927

Vancouver

Friedrich A. Concentration of small Hawking type surfaces. Differential Geometry and its Application. 2022;85:1-23. 101927. https://doi.org/10.1016/j.difgeo.2022.101927

Author

Friedrich, Alexander. / Concentration of small Hawking type surfaces. In: Differential Geometry and its Application. 2022 ; Vol. 85. pp. 1-23.

Bibtex

@article{9e81e6f55be34364bdbf5c752f8c9cbb,
title = "Concentration of small Hawking type surfaces",
abstract = "We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble trees. These bubble trees are smooth spheres provided their area is small enough. Following a similar analysis of the Willmore functional conducted by T. Lamm and J. Metzger we characterize the concentration points of area constrained, critical surfaces for Hawking type functionals and the Hawking energy. Moreover, we determine their expansion on small surfaces.",
keywords = "Hawking energy, Mathematical general relativity, Quasi-local energy, Willmore functional",
author = "Alexander Friedrich",
note = "Publisher Copyright: {\textcopyright} 2022",
year = "2022",
doi = "10.1016/j.difgeo.2022.101927",
language = "English",
volume = "85",
pages = "1--23",
journal = "Differential Geometry and its Applications",
issn = "0926-2245",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Concentration of small Hawking type surfaces

AU - Friedrich, Alexander

N1 - Publisher Copyright: © 2022

PY - 2022

Y1 - 2022

N2 - We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble trees. These bubble trees are smooth spheres provided their area is small enough. Following a similar analysis of the Willmore functional conducted by T. Lamm and J. Metzger we characterize the concentration points of area constrained, critical surfaces for Hawking type functionals and the Hawking energy. Moreover, we determine their expansion on small surfaces.

AB - We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble trees. These bubble trees are smooth spheres provided their area is small enough. Following a similar analysis of the Willmore functional conducted by T. Lamm and J. Metzger we characterize the concentration points of area constrained, critical surfaces for Hawking type functionals and the Hawking energy. Moreover, we determine their expansion on small surfaces.

KW - Hawking energy

KW - Mathematical general relativity

KW - Quasi-local energy

KW - Willmore functional

UR - http://www.scopus.com/inward/record.url?scp=85136070987&partnerID=8YFLogxK

U2 - 10.1016/j.difgeo.2022.101927

DO - 10.1016/j.difgeo.2022.101927

M3 - Journal article

AN - SCOPUS:85136070987

VL - 85

SP - 1

EP - 23

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

SN - 0926-2245

M1 - 101927

ER -

ID: 317811910