id	sid	tid	token	lemma	pos
m900ns09h4s	1	1	riemannian	riemannian	ADJ
m900ns09h4s	1	2	metrics	metric	NOUN
m900ns09h4s	1	3	that	that	PRON
m900ns09h4s	1	4	extremize	extremize	VERB
m900ns09h4s	1	5	eigenvalues	eigenvalue	NOUN
m900ns09h4s	1	6	of	of	ADP
m900ns09h4s	1	7	conformally	conformally	ADV
m900ns09h4s	1	8	covariant	covariant	NOUN
m900ns09h4s	1	9	operators	operator	NOUN
m900ns09h4s	1	10	are	be	AUX
m900ns09h4s	1	11	known	know	VERB
m900ns09h4s	1	12	to	to	PART
m900ns09h4s	1	13	have	have	VERB
m900ns09h4s	1	14	a	a	DET
m900ns09h4s	1	15	relationship	relationship	NOUN
m900ns09h4s	1	16	with	with	ADP
m900ns09h4s	1	17	the	the	DET
m900ns09h4s	1	18	existence	existence	NOUN
m900ns09h4s	1	19	of	of	ADP
m900ns09h4s	1	20	solutions	solution	NOUN
m900ns09h4s	1	21	of	of	ADP
m900ns09h4s	1	22	important	important	ADJ
m900ns09h4s	1	23	partial	partial	ADJ
m900ns09h4s	1	24	differential	differential	ADJ
m900ns09h4s	1	25	equations	equation	NOUN
m900ns09h4s	1	26	(	(	PUNCT
m900ns09h4s	1	27	pdes	pde	NOUN
m900ns09h4s	1	28	)	)	PUNCT
m900ns09h4s	1	29	.	.	PUNCT
m900ns09h4s	2	1	on	on	ADP
m900ns09h4s	2	2	compact	compact	ADJ
m900ns09h4s	2	3	surfaces	surface	NOUN
m900ns09h4s	2	4	with	with	ADP
m900ns09h4s	2	5	no	no	DET
m900ns09h4s	2	6	boundary	boundary	NOUN
m900ns09h4s	2	7	,	,	PUNCT
m900ns09h4s	2	8	the	the	DET
m900ns09h4s	2	9	study	study	NOUN
m900ns09h4s	2	10	of	of	ADP
m900ns09h4s	2	11	such	such	ADJ
m900ns09h4s	2	12	extremal	extremal	ADJ
m900ns09h4s	2	13	metrics	metric	NOUN
m900ns09h4s	2	14	for	for	ADP
m900ns09h4s	2	15	the	the	DET
m900ns09h4s	2	16	laplace	laplace	PROPN
m900ns09h4s	2	17	-	-	PUNCT
m900ns09h4s	2	18	beltrami	beltrami	PROPN
m900ns09h4s	2	19	operator	operator	NOUN
m900ns09h4s	2	20	has	have	AUX
m900ns09h4s	2	21	led	lead	VERB
m900ns09h4s	2	22	mathematicians	mathematician	NOUN
m900ns09h4s	2	23	to	to	ADP
m900ns09h4s	2	24	special	special	ADJ
m900ns09h4s	2	25	examples	example	NOUN
m900ns09h4s	2	26	of	of	ADP
m900ns09h4s	2	27	minimal	minimal	ADJ
m900ns09h4s	2	28	surfaces	surface	NOUN
m900ns09h4s	2	29	and	and	CCONJ
m900ns09h4s	2	30	harmonic	harmonic	ADJ
m900ns09h4s	2	31	maps	map	NOUN
m900ns09h4s	2	32	into	into	ADP
m900ns09h4s	2	33	spheres	sphere	NOUN
m900ns09h4s	2	34	.	.	PUNCT
m900ns09h4s	3	1	this	this	DET
m900ns09h4s	3	2	thesis	thesis	NOUN
m900ns09h4s	3	3	is	be	AUX
m900ns09h4s	3	4	devoted	devote	VERB
m900ns09h4s	3	5	to	to	ADP
m900ns09h4s	3	6	the	the	DET
m900ns09h4s	3	7	study	study	NOUN
m900ns09h4s	3	8	of	of	ADP
m900ns09h4s	3	9	the	the	DET
m900ns09h4s	3	10	existence	existence	NOUN
m900ns09h4s	3	11	and	and	CCONJ
m900ns09h4s	3	12	properties	property	NOUN
m900ns09h4s	3	13	of	of	ADP
m900ns09h4s	3	14	extremal	extremal	ADJ
m900ns09h4s	3	15	metrics	metric	NOUN
m900ns09h4s	3	16	for	for	ADP
m900ns09h4s	3	17	other	other	ADJ
m900ns09h4s	3	18	natural	natural	ADJ
m900ns09h4s	3	19	and	and	CCONJ
m900ns09h4s	3	20	geometrically	geometrically	ADV
m900ns09h4s	3	21	defined	define	VERB
m900ns09h4s	3	22	differential	differential	ADJ
m900ns09h4s	3	23	operators	operator	NOUN
m900ns09h4s	3	24	.	.	PUNCT
m900ns09h4s	4	1	questions	question	NOUN
m900ns09h4s	4	2	about	about	ADP
m900ns09h4s	4	3	the	the	DET
m900ns09h4s	4	4	regularity	regularity	NOUN
m900ns09h4s	4	5	of	of	ADP
m900ns09h4s	4	6	extremal	extremal	ADJ
m900ns09h4s	4	7	metrics	metric	NOUN
m900ns09h4s	4	8	,	,	PUNCT
m900ns09h4s	4	9	possible	possible	ADJ
m900ns09h4s	4	10	obstructions	obstruction	NOUN
m900ns09h4s	4	11	to	to	ADP
m900ns09h4s	4	12	their	their	PRON
m900ns09h4s	4	13	existence	existence	NOUN
m900ns09h4s	4	14	,	,	PUNCT
m900ns09h4s	4	15	and	and	CCONJ
m900ns09h4s	4	16	to	to	ADP
m900ns09h4s	4	17	which	which	PRON
m900ns09h4s	4	18	pdes	pde	NOUN
m900ns09h4s	4	19	are	be	AUX
m900ns09h4s	4	20	these	these	PRON
m900ns09h4s	4	21	associated	associate	VERB
m900ns09h4s	4	22	with	with	ADP
m900ns09h4s	4	23	are	be	AUX
m900ns09h4s	4	24	discussed	discuss	VERB
m900ns09h4s	4	25	.	.	PUNCT