Class information for:
Level 1: POLYA SZEGO INEQUALITY//MANIFOLDS WITH DENSITY//STEINER SYMMETRIZATION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
20218 471 19.8 38%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
94 3       MATHEMATICS//MATHEMATICS, APPLIED//MATH 76582
176 2             MATHEMATICS//VARIATIONAL METHODS//MATHEMATICS, APPLIED 22137
20218 1                   POLYA SZEGO INEQUALITY//MANIFOLDS WITH DENSITY//STEINER SYMMETRIZATION 471

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 POLYA SZEGO INEQUALITY authKW 345754 2% 67% 8
2 MANIFOLDS WITH DENSITY authKW 333409 1% 86% 6
3 STEINER SYMMETRIZATION authKW 304324 3% 36% 13
4 CHEEGER SETS authKW 291726 2% 50% 9
5 RELATIVE ISOPERIMETRIC INEQUALITIES authKW 259320 1% 100% 4
6 ISOPERIMETRIC INEQUALITY authKW 217841 7% 10% 33
7 QUANTITATIVE ISOPERIMETRIC INEQUALITY authKW 207454 1% 80% 4
8 ISOPERIMETRIC PROBLEM authKW 195465 3% 22% 14
9 FENCING PROBLEMS authKW 194490 1% 100% 3
10 FRAENKEL ASYMMETRY authKW 194490 1% 100% 3

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 16801 80% 0% 379
2 Mathematics, Applied 4512 39% 0% 184
3 Automation & Control Systems 41 2% 0% 11
4 Statistics & Probability 32 3% 0% 12
5 Mechanics 17 3% 0% 15
6 Operations Research & Management Science 6 1% 0% 6
7 Computer Science, Software Engineering 3 1% 0% 5
8 Physics, Mathematical 2 1% 0% 6
9 Imaging Science & Photographic Technology 1 0% 0% 2
10 Computer Science, Theory & Methods 1 1% 0% 5

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 HUE GEOMETRY GRP 86439 0% 67% 2
2 CINCIAS EXATAS LICADAS 64830 0% 100% 1
3 DIPARTIMENTO MATEMAT LICAZ R CACCIOPPOLI 64830 0% 100% 1
4 GALILES 64830 0% 100% 1
5 GRENOBLE FOURIER 64830 0% 100% 1
6 INSITUTE SYST THEORY AUTOMAT CONTROL 64830 0% 100% 1
7 KWANACK GU 64830 0% 100% 1
8 MATH UMR 5127 64830 0% 100% 1
9 MATIQUES PLIQU 64830 0% 100% 1
10 ST PETERSBURG BRANCHM 64830 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 21497 5% 1% 23
2 JOURNAL OF GEOMETRIC ANALYSIS 14013 3% 2% 14
3 JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 6086 2% 1% 8
4 JOURNAL OF CONVEX ANALYSIS 4854 2% 1% 8
5 ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS 4028 1% 1% 7
6 ADVANCES IN CALCULUS OF VARIATIONS 3833 1% 2% 3
7 COMMUNICATIONS IN ANALYSIS AND GEOMETRY 3765 1% 1% 6
8 RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA 2898 1% 1% 4
9 AMERICAN MATHEMATICAL MONTHLY 2887 2% 0% 11
10 ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE 2571 1% 1% 7

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 POLYA SZEGO INEQUALITY 345754 2% 67% 8 Search POLYA+SZEGO+INEQUALITY Search POLYA+SZEGO+INEQUALITY
2 MANIFOLDS WITH DENSITY 333409 1% 86% 6 Search MANIFOLDS+WITH+DENSITY Search MANIFOLDS+WITH+DENSITY
3 STEINER SYMMETRIZATION 304324 3% 36% 13 Search STEINER+SYMMETRIZATION Search STEINER+SYMMETRIZATION
4 CHEEGER SETS 291726 2% 50% 9 Search CHEEGER+SETS Search CHEEGER+SETS
5 RELATIVE ISOPERIMETRIC INEQUALITIES 259320 1% 100% 4 Search RELATIVE+ISOPERIMETRIC+INEQUALITIES Search RELATIVE+ISOPERIMETRIC+INEQUALITIES
6 ISOPERIMETRIC INEQUALITY 217841 7% 10% 33 Search ISOPERIMETRIC+INEQUALITY Search ISOPERIMETRIC+INEQUALITY
7 QUANTITATIVE ISOPERIMETRIC INEQUALITY 207454 1% 80% 4 Search QUANTITATIVE+ISOPERIMETRIC+INEQUALITY Search QUANTITATIVE+ISOPERIMETRIC+INEQUALITY
8 ISOPERIMETRIC PROBLEM 195465 3% 22% 14 Search ISOPERIMETRIC+PROBLEM Search ISOPERIMETRIC+PROBLEM
9 FENCING PROBLEMS 194490 1% 100% 3 Search FENCING+PROBLEMS Search FENCING+PROBLEMS
10 FRAENKEL ASYMMETRY 194490 1% 100% 3 Search FRAENKEL+ASYMMETRY Search FRAENKEL+ASYMMETRY

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 FUSCO, N , (2015) THE QUANTITATIVE ISOPERIMETRIC INEQUALITY AND RELATED TOPICS.BULLETIN OF MATHEMATICAL SCIENCES. VOL. 5. ISSUE 3. P. 517 -607 44 64% 2
2 CICALESE, M , LEONARDI, GP , (2013) BEST CONSTANTS FOR THE ISOPERIMETRIC INEQUALITY IN QUANTITATIVE FORM.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. VOL. 15. ISSUE 3. P. 1101 -1129 17 94% 3
3 CABRE, X , ROS-OTON, X , SERRA, J , (2016) SHARP ISOPERIMETRIC INEQUALITIES VIA THE ABP.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. VOL. 18. ISSUE 12. P. 2971 -2998 21 70% 0
4 NEUMAYER, R , (2016) A STRONG FORM OF THE QUANTITATIVE WULFF INEQUALITY.SIAM JOURNAL ON MATHEMATICAL ANALYSIS. VOL. 48. ISSUE 3. P. 1727 -1772 17 74% 1
5 BROCK, F , CHIACCHIO, F , MERCALDO, A , (2014) A WEIGHTED ISOPERIMETRIC INEQUALITY IN AN ORTHANT.POTENTIAL ANALYSIS. VOL. 41. ISSUE 1. P. 171 -186 16 80% 3
6 BIANCHINI, C , CROCE, G , HENROT, A , (2017) ON THE QUANTITATIVE ISOPERIMETRIC INEQUALITY IN THE PLANE.ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS. VOL. 23. ISSUE 2. P. 517 -549 12 100% 0
7 FIGALLI, A , MAGGI, F , PRATELLI, A , (2009) A NOTE ON CHEEGER SETS.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 137. ISSUE 6. P. 2057 -2062 16 84% 14
8 FIGALLI, A , MAGGI, F , (2013) ON THE ISOPERIMETRIC PROBLEM FOR RADIAL LOG-CONVEX DENSITIES.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. VOL. 48. ISSUE 3-4. P. 447 -489 15 79% 7
9 CICALESE, M , LEONARDI, GP , (2012) A SELECTION PRINCIPLE FOR THE SHARP QUANTITATIVE ISOPERIMETRIC INEQUALITY.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. VOL. 206. ISSUE 2. P. 617-643 14 78% 28
10 CANETE, A , ROSALES, C , (2014) COMPACT STABLE HYPERSURFACES WITH FREE BOUNDARY IN CONVEX SOLID CONES WITH HOMOGENEOUS DENSITIES.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. VOL. 51. ISSUE 3-4. P. 887 -913 17 63% 4

Classes with closest relation at Level 1


Rank Class id link
1 13757 UNIVERSAL INEQUALITIES//EIGENVALUE RATIO//LIEB THIRRING INEQUALITIES
2 33278 Q VALUED FUNCTIONS//FINITE SUBSET SPACE//MULTIPLE VALUED FUNCTIONS
3 29291 CONDENSER CAPACITY//CIRCULAR SYMMETRIZATION//LOGARITHMIC CAPACITY
4 14755 RENORMALIZED FUNCTIONAL//EQUAL AREA CONDITION//ALLEN CAHN EQUATION
5 22762 TWO PHASE CONDUCTORS//REARRANGEMENTS OF A FUNCTION//NANOSTRUCTURED QUANTUM DOTS
6 22194 CAPILLARY SURFACE//CONCUS FINN CONJECTURE//CAPILLARY GRAPH
7 4326 CONVEX BODY//STAR BODY//INTERSECTION BODY
8 10729 RENORMALIZED SOLUTIONS//L 1 DATA//RELATIVE REARRANGEMENT
9 34062 CURVATURE BOUNDED ABOVE//CATK SPACES//LAMBDA CONVEX SET
10 17321 OVERDETERMINED PROBLEMS//POMPEIU PROBLEM//OVERDETERMINED BOUNDARY VALUE PROBLEMS

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