Class information for:
Level 1: SUB RIEMANNIAN GEOMETRY//CARNOT GROUPS//HEISENBERG GROUP

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
5583 1601 23.5 40%


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
2042 2             SUB RIEMANNIAN GEOMETRY//CARNOT GROUPS//LIPSCHITZ DOMAINS 5373
5583 1                   SUB RIEMANNIAN GEOMETRY//CARNOT GROUPS//HEISENBERG GROUP 1601

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 SUB RIEMANNIAN GEOMETRY authKW 1463384 7% 71% 108
2 CARNOT GROUPS authKW 969898 5% 63% 81
3 HEISENBERG GROUP authKW 579506 8% 24% 128
4 SUB LAPLACIAN authKW 439467 2% 59% 39
5 CARNOT CARATHEODORY METRIC authKW 297740 1% 71% 22
6 HORMANDERS VECTOR FIELDS authKW 286065 1% 100% 15
7 CR PANEITZ OPERATOR authKW 228852 1% 100% 12
8 CARNOT CARATHEODORY SPACE authKW 211969 1% 65% 17
9 PSEUDOHERMITIAN MANIFOLD authKW 209781 1% 100% 11
10 STRATIFIED GROUPS authKW 201432 1% 81% 13

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 67386 87% 0% 1397
2 Mathematics, Applied 14215 38% 0% 603
3 Automation & Control Systems 526 4% 0% 66
4 Physics, Mathematical 14 2% 0% 25
5 Computer Science, Artificial Intelligence 8 1% 0% 20
6 Computer Science, Software Engineering 3 1% 0% 13
7 Computer Science, Cybernetics 2 0% 0% 3
8 Imaging Science & Photographic Technology -0 0% 0% 3
9 Statistics & Probability -1 0% 0% 6
10 Mathematics, Interdisciplinary Applications -1 0% 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 DIPARTMENTO MATEMAT 123759 4% 9% 72
2 NUMER SIMULAT TECHNOL JIANGXI PROV 79461 0% 83% 5
3 DIPARTIMENTO MATEMAT 78930 15% 2% 239
4 PROGRAM SYST 52575 1% 14% 20
5 SOBOLEV MATH 50198 3% 5% 50
6 CNRS 5219 34325 0% 60% 3
7 DIPARTIMENTO METODI MATEMAT 25427 0% 67% 2
8 IST E 25427 0% 67% 2
9 DIPARTIMENTO INGN GEST INFORMAZ 23466 0% 31% 4
10 2750 21451 0% 38% 3

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 JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS 45569 2% 7% 32
2 JOURNAL OF GEOMETRIC ANALYSIS 25747 2% 4% 35
3 SIBERIAN MATHEMATICAL JOURNAL 22684 4% 2% 60
4 ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 21968 1% 5% 24
5 POTENTIAL ANALYSIS 21958 2% 3% 34
6 COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 13836 3% 2% 42
7 CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 11451 2% 2% 31
8 DOKLADY MATHEMATICS 10936 3% 1% 42
9 REVISTA MATEMATICA IBEROAMERICANA 7248 1% 2% 17
10 ANNALI DI MATEMATICA PURA ED APPLICATA 7005 1% 2% 23

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 SUB RIEMANNIAN GEOMETRY 1463384 7% 71% 108 Search SUB+RIEMANNIAN+GEOMETRY Search SUB+RIEMANNIAN+GEOMETRY
2 CARNOT GROUPS 969898 5% 63% 81 Search CARNOT+GROUPS Search CARNOT+GROUPS
3 HEISENBERG GROUP 579506 8% 24% 128 Search HEISENBERG+GROUP Search HEISENBERG+GROUP
4 SUB LAPLACIAN 439467 2% 59% 39 Search SUB+LAPLACIAN Search SUB+LAPLACIAN
5 CARNOT CARATHEODORY METRIC 297740 1% 71% 22 Search CARNOT+CARATHEODORY+METRIC Search CARNOT+CARATHEODORY+METRIC
6 HORMANDERS VECTOR FIELDS 286065 1% 100% 15 Search HORMANDERS+VECTOR+FIELDS Search HORMANDERS+VECTOR+FIELDS
7 CR PANEITZ OPERATOR 228852 1% 100% 12 Search CR+PANEITZ+OPERATOR Search CR+PANEITZ+OPERATOR
8 CARNOT CARATHEODORY SPACE 211969 1% 65% 17 Search CARNOT+CARATHEODORY+SPACE Search CARNOT+CARATHEODORY+SPACE
9 PSEUDOHERMITIAN MANIFOLD 209781 1% 100% 11 Search PSEUDOHERMITIAN+MANIFOLD Search PSEUDOHERMITIAN+MANIFOLD
10 STRATIFIED GROUPS 201432 1% 81% 13 Search STRATIFIED+GROUPS Search STRATIFIED+GROUPS

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 CAPOGNA, L , CITTI, G , (2016) REGULARITY FOR SUBELLIPTIC PDE THROUGH UNIFORM ESTIMATES IN MULTI-SCALE GEOMETRIES.BULLETIN OF MATHEMATICAL SCIENCES. VOL. 6. ISSUE 2. P. 173 -230 52 90% 0
2 CASSANO, FS , VITTONE, D , (2014) GRAPHS OF BOUNDED VARIATION, EXISTENCE AND LOCAL BOUNDEDNESS OF NON-PARAMETRIC MINIMAL SURFACES IN HEISENBERG GROUPS.ADVANCES IN CALCULUS OF VARIATIONS. VOL. 7. ISSUE 4. P. 409 -492 41 98% 3
3 GALLI, M , (2016) THE REGULARITY OF EUCLIDEAN LIPSCHITZ BOUNDARIES WITH PRESCRIBED MEAN CURVATURE IN THREE-DIMENSIONAL CONTACT SUB-RIEMANNIAN MANIFOLDS.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. VOL. 136. ISSUE . P. 40 -50 33 100% 0
4 VITTONE, D , (2012) LIPSCHITZ SURFACES, PERIMETER AND TRACE THEOREMS FOR BV FUNCTIONS IN CARNOT-CARATHEODORY SPACES.ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE. VOL. 11. ISSUE 4. P. 939-998 34 97% 4
5 IVANOV, S , VASSILEV, D , (2015) THE LICHNEROWICZ AND OBATA FIRST EIGENVALUE THEOREMS AND THE OBATA UNIQUENESS RESULT IN THE YAMABE PROBLEM ON CR AND QUATERNIONIC CONTACT MANIFOLDS.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS. VOL. 126. ISSUE . P. 262 -323 55 53% 1
6 DANIELLI, D , GAROFALO, N , NHIEU, DM , (2010) SUB-RIEMANNIAN CALCULUS AND MONOTONICITY OF THE PERIMETER FOR GRAPHICAL STRIPS.MATHEMATISCHE ZEITSCHRIFT. VOL. 265. ISSUE 3. P. 617 -637 35 90% 1
7 CITTI, G , MANFREDINI, M , PINAMONTI, A , CASSANO, FS , (2016) POINCARE-TYPE INEQUALITY FOR LIPSCHITZ CONTINUOUS VECTOR FIELDS.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES. VOL. 105. ISSUE 3. P. 265 -292 30 91% 0
8 MAGNANI, V , SCIENZA, M , (2016) REGULARITY ESTIMATES FOR CONVEX FUNCTIONS IN CARNOT-CARATHEODORY SPACES.REVISTA MATEMATICA IBEROAMERICANA. VOL. 32. ISSUE 3. P. 835 -858 28 93% 0
9 HURTADO, A , ROSALES, C , (2015) EXISTENCE, CHARACTERIZATION AND STABILITY OF PANSU SPHERES IN SUB-RIEMANNIAN 3-SPACE FORMS.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. VOL. 54. ISSUE 3. P. 3183 -3227 30 88% 0
10 (2006) NON-DOUBLING AHLFORS MEASURES, PERIMETER MEASURES, AND THE CHARACTERIZATION OF THE TRACE SPACES OF SOBOLEV FUNCTIONS IN CARNOT-CARATHEODORY SPACES - INTRODUCTION.MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 182. ISSUE 857. P. 1-+ 58 56% 0

Classes with closest relation at Level 1


Rank Class id link
1 6534 DOUBLING MEASURE//ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA//QUASIHYPERBOLIC METRIC
2 5559 RIESZ TRANSFORM//SPECTRAL MULTIPLIERS//HARDY SPACE
3 6655 REIFENBERG DOMAIN//PARTIAL REGULARITY//CALDERON ZYGMUND ESTIMATES
4 13801 INFINITY LAPLACIAN//VISCOSITY SOLUTIONS//FULLY NONLINEAR EQUATIONS
5 26009 REGULAR SYNTHESIS//SINGULAR CHARACTERISTICS//FOLD AND SIMPLE CUSP SINGULARITIES
6 24807 FINELY SUPERHARMONIC FUNCTION//PWB SOLUTION//HOMOGENEOUS RANDOM MEASURE
7 7600 Q CURVATURE//CRITICAL POINTS AT INFINITY//YAMABE PROBLEM
8 36205 OVERDETERMINATION CONDITION//ULTRAPARABOLIC EQUATIONS//ANISOTROPIC UNIQUENESS CLASS
9 17525 COMPLEX VECTOR FIELDS//NON COMMUTATIVE HARMONIC OSCILLATOR//HYPOELLIPTICITY
10 25247 TRUDINGER MOSER INEQUALITY//MOSER TRUDINGER INEQUALITY//BLOWING UP ANALYSIS

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