id	sid	tid	token	lemma	pos
6w924b31b4f	1	1	in	in	ADP
6w924b31b4f	1	2	this	this	DET
6w924b31b4f	1	3	thesis	thesis	NOUN
6w924b31b4f	1	4	,	,	PUNCT
6w924b31b4f	1	5	we	we	PRON
6w924b31b4f	1	6	study	study	VERB
6w924b31b4f	1	7	the	the	DET
6w924b31b4f	1	8	boundary	boundary	ADJ
6w924b31b4f	1	9	-	-	PUNCT
6w924b31b4f	1	10	blow	blow	NOUN
6w924b31b4f	1	11	-	-	PUNCT
6w924b31b4f	1	12	up	up	ADP
6w924b31b4f	1	13	problem	problem	NOUN
6w924b31b4f	1	14	for	for	ADP
6w924b31b4f	1	15	the	the	DET
6w924b31b4f	1	16	negative	negative	ADJ
6w924b31b4f	1	17	$	$	SYM
6w924b31b4f	1	18	sigma_k$-ricci	sigma_k$-ricci	NOUN
6w924b31b4f	1	19	equations	equation	NOUN
6w924b31b4f	1	20	in	in	ADP
6w924b31b4f	1	21	bounded	bounded	ADJ
6w924b31b4f	1	22	domains	domain	NOUN
6w924b31b4f	1	23	of	of	ADP
6w924b31b4f	1	24	r^n	r^n	NOUN
6w924b31b4f	1	25	.	.	NOUN
6w924b31b4f	1	26	by	by	ADP
6w924b31b4f	1	27	adopting	adopt	VERB
6w924b31b4f	1	28	the	the	DET
6w924b31b4f	1	29	method	method	NOUN
6w924b31b4f	1	30	of	of	ADP
6w924b31b4f	1	31	loewner	loewner	NOUN
6w924b31b4f	1	32	-	-	PUNCT
6w924b31b4f	1	33	nirenberg	nirenberg	PROPN
6w924b31b4f	1	34	for	for	ADP
6w924b31b4f	1	35	the	the	DET
6w924b31b4f	1	36	scalar	scalar	ADJ
6w924b31b4f	1	37	curvature	curvature	NOUN
6w924b31b4f	1	38	,	,	PUNCT
6w924b31b4f	1	39	we	we	PRON
6w924b31b4f	1	40	generalize	generalize	VERB
6w924b31b4f	1	41	their	their	PRON
6w924b31b4f	1	42	results	result	NOUN
6w924b31b4f	1	43	to	to	ADP
6w924b31b4f	1	44	the	the	DET
6w924b31b4f	1	45	negative	negative	ADJ
6w924b31b4f	1	46	$	$	SYM
6w924b31b4f	1	47	sigma_k$-ricci	sigma_k$-ricci	NOUN
6w924b31b4f	1	48	equations	equation	NOUN
6w924b31b4f	1	49	.	.	PUNCT
6w924b31b4f	2	1	when	when	SCONJ
6w924b31b4f	2	2	$	$	SYM
6w924b31b4f	2	3	k=1,2,$	k=1,2,$	NOUN
6w924b31b4f	2	4	and	and	CCONJ
6w924b31b4f	2	5	$	$	SYM
6w924b31b4f	2	6	n$	n$	NOUN
6w924b31b4f	2	7	,	,	PUNCT
6w924b31b4f	2	8	the	the	DET
6w924b31b4f	2	9	necessary	necessary	ADJ
6w924b31b4f	2	10	condition	condition	NOUN
6w924b31b4f	2	11	for	for	ADP
6w924b31b4f	2	12	the	the	DET
6w924b31b4f	2	13	existence	existence	NOUN
6w924b31b4f	2	14	of	of	ADP
6w924b31b4f	2	15	the	the	DET
6w924b31b4f	2	16	solutions	solution	NOUN
6w924b31b4f	2	17	satisfying	satisfy	VERB
6w924b31b4f	2	18	the	the	DET
6w924b31b4f	2	19	$	$	SYM
6w924b31b4f	2	20	sigma_k$-ricci	sigma_k$-ricci	PROPN
6w924b31b4f	2	21	equations	equation	NOUN
6w924b31b4f	2	22	is	be	AUX
6w924b31b4f	2	23	that	that	SCONJ
6w924b31b4f	2	24	the	the	DET
6w924b31b4f	2	25	codimension	codimension	NOUN
6w924b31b4f	2	26	of	of	ADP
6w924b31b4f	2	27	the	the	DET
6w924b31b4f	2	28	portion	portion	NOUN
6w924b31b4f	2	29	of	of	ADP
6w924b31b4f	2	30	boundary	boundary	NOUN
6w924b31b4f	2	31	has	have	VERB
6w924b31b4f	2	32	to	to	PART
6w924b31b4f	2	33	be	be	AUX
6w924b31b4f	2	34	bounded	bound	VERB
6w924b31b4f	2	35	from	from	ADP
6w924b31b4f	2	36	above	above	ADV
6w924b31b4f	2	37	by	by	ADP
6w924b31b4f	2	38	some	some	DET
6w924b31b4f	2	39	constants	constant	NOUN
6w924b31b4f	2	40	depending	depend	VERB
6w924b31b4f	2	41	on	on	ADP
6w924b31b4f	2	42	$	$	SYM
6w924b31b4f	2	43	n$	n$	NOUN
6w924b31b4f	2	44	and	and	CCONJ
6w924b31b4f	2	45	$	$	SYM
6w924b31b4f	2	46	k$.	k$.	X
6w924b31b4f	2	47	for	for	ADP
6w924b31b4f	2	48	other	other	ADJ
6w924b31b4f	2	49	cases	case	NOUN
6w924b31b4f	2	50	,	,	PUNCT
6w924b31b4f	2	51	we	we	PRON
6w924b31b4f	2	52	believe	believe	VERB
6w924b31b4f	2	53	that	that	SCONJ
6w924b31b4f	2	54	the	the	DET
6w924b31b4f	2	55	similar	similar	ADJ
6w924b31b4f	2	56	argument	argument	NOUN
6w924b31b4f	2	57	can	can	AUX
6w924b31b4f	2	58	be	be	AUX
6w924b31b4f	2	59	developed	develop	VERB
6w924b31b4f	2	60	.	.	PUNCT