The sell-off proposals have prompted strong opposition
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A section of Hearts fans angry at plans to sell the Tynecastle ground and move to Murrayfield have been warned to stay within the law by police.
The notice from Lothian and Borders Police follows threats to several of the Edinburgh club's directors.
Police said there have been "several unsavoury" incidents at their homes.
Gary Mackay, a former Hearts captain and strong opponent of the move, said protests must be legal but urged the board to resign.
An extraordinary meeting of Hearts shareholders will on Monday discuss a proposal to sell the ground for £22m to housing developer Cala Management.
Under the scheme, the club would groundshare at Murrayfield while work on finding and investing in a new ground was completed.
However, the proposals have provoked a storm of protest against the board and an extreme reaction among some of the debt-hit Scottish Premier League club's fans.
'Nasty behaviour'
Superintendent Terry Powell said: "We've had a range of unsavoury incidents at the homes of either directors or shareholders of the club.
"This has included hate mail, intimidation of their families by surrounding their houses and there's been some graffiti.
"It's generally nasty behaviour which has frightened some of the families quite badly."
Mr Mackay said fans must be law-abiding in opposing the plans.
"We have to make sure we're vociferous, we're strong in venting our feelings but we do not turn to violence, that just doesn't get anybody anywhere," he said.
"We must continue to make sure the board realise that we want them removed from office."
Opponents of the sell-off released black balloons in Tynecastle as a sign of their displeasure during Sunday's clash with Rangers, which ended scoreless.