A uniform sublevel set estimate

Anthony Carbery

A uniform sublevel set estimate

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract / Description of output

We prove that there is an absolute constant C depending only on the dimension n so that if u is a non-negative strictly convex smooth function defined on a convex body in R-n the determinant of whose hessian is bounded below by 1, then the volume of the sublevel set of u of height s is at most Cs-n/2.

Original language	English
Title of host publication	HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS
Editors	P Cifuentes, J GarciaCuerva, G Garrigos, E Hernandez, JM Martell, J Parcet, A Ruiz, F Soria, JL Torea, A Vargas
Place of Publication	PROVIDENCE
Publisher	American Mathematical Society
Pages	97-103
Number of pages	7
ISBN (Print)	978-0-8218-4770-1
Publication status	Published - 2008

Keywords / Materials (for Non-textual outputs)

Sublevel sets
convex functions
affine isoperimetric inequalities
VAN

Cite this

@inproceedings{830e93c148e4418ca387ff30bb131872,

title = "A uniform sublevel set estimate",

abstract = "We prove that there is an absolute constant C depending only on the dimension n so that if u is a non-negative strictly convex smooth function defined on a convex body in R-n the determinant of whose hessian is bounded below by 1, then the volume of the sublevel set of u of height s is at most Cs-n/2.",

keywords = "Sublevel sets, convex functions, affine isoperimetric inequalities, VAN",

author = "Anthony Carbery",

year = "2008",

language = "English",

isbn = "978-0-8218-4770-1",

pages = "97--103",

editor = "P Cifuentes and J GarciaCuerva and G Garrigos and E Hernandez and JM Martell and J Parcet and A Ruiz and F Soria and JL Torea and A Vargas",

booktitle = "HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS",

publisher = "American Mathematical Society",

address = "United States",

}

A uniform sublevel set estimate. / Carbery, Anthony.
HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS. ed. / P Cifuentes; J GarciaCuerva; G Garrigos; E Hernandez; JM Martell; J Parcet; A Ruiz; F Soria; JL Torea; A Vargas. PROVIDENCE: American Mathematical Society, 2008. p. 97-103.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A uniform sublevel set estimate

AU - Carbery, Anthony

PY - 2008

Y1 - 2008

N2 - We prove that there is an absolute constant C depending only on the dimension n so that if u is a non-negative strictly convex smooth function defined on a convex body in R-n the determinant of whose hessian is bounded below by 1, then the volume of the sublevel set of u of height s is at most Cs-n/2.

AB - We prove that there is an absolute constant C depending only on the dimension n so that if u is a non-negative strictly convex smooth function defined on a convex body in R-n the determinant of whose hessian is bounded below by 1, then the volume of the sublevel set of u of height s is at most Cs-n/2.

KW - Sublevel sets

KW - convex functions

KW - affine isoperimetric inequalities

KW - VAN

M3 - Conference contribution

SN - 978-0-8218-4770-1

SP - 97

EP - 103

BT - HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS

A2 - Cifuentes, P

A2 - GarciaCuerva, J

A2 - Garrigos, G

A2 - Hernandez, E

A2 - Martell, JM

A2 - Parcet, J

A2 - Ruiz, A

A2 - Soria, F

A2 - Torea, JL

A2 - Vargas, A

PB - American Mathematical Society

CY - PROVIDENCE

ER -

A uniform sublevel set estimate

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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